equation_gpt_train_geometry.jsonl

{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_2</equation> in Area of a Trapezoid is: Length of bottom of trapezoid.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>x_2</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Polar Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>r</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>A</equation> in Area of a Rectangle is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Rectangle?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>B</equation> in Plane is: Coefficient of y.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>B</equation> in Plane?"}
{"completion": " The Latex Code for equation Elliptic Coneis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Elliptic Cone?"}
{"completion": " The equation for Distance Between Two Points 3D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 3D:\n        Latex code for Distance Between Two Points 3D.\n        \n: Distance\n: Point 1\n: Point 2\n: Point 3\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Distance Between Two Points 3D?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>b</equation> in Elliptic Cone is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>b</equation> in Elliptic Cone?"}
{"completion": " The equation for Area of a Sector is: <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. Here is the brief introduction of Area of a Sector:\n        Latex code for Area of a Sector.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Sector?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>x</equation> in Surface area of a cube is: Length of a square.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>x</equation> in Surface area of a cube?"}
{"completion": " The Latex Code for equation Ellipsoidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Ellipsoid?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 3D is: Point 2.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 2D is: Distance.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>d</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Eccentricity of an Ellipse is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of an Ellipse:\n        Latex code for Eccentricity of an Ellipse.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Eccentricity of an Ellipse?"}
{"completion": " The equation for Cartesian to Polar Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Polar Coordinates:\n        Latex code for Cartesian to Polar Coordinates.\n        \n: Polar Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Cartesian to Polar Coordinates?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>h</equation> in Area of a Parallelogram is: Length of Height of parallelogram.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>h</equation> in Area of a Parallelogram?"}
{"completion": " The Latex Code for equation Surface area of a cylinderis <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Surface area of a cylinder?"}
{"completion": " The equation for Area of a Parallelogram is: <equation>A = bh</equation>. Here is the brief introduction of Area of a Parallelogram:\n        Latex code for Area of a Parallelogram.\n        \n: Area\n: Length of Base\n: Length of Height of parallelogram\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Parallelogram?"}
{"completion": " The equation for Area of a Equilateral Triangle is <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. The meaning of symbol <equation>A</equation> in Area of a Equilateral Triangle is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Equilateral Triangle?"}
{"completion": " The equation for Area of a Rhombus is <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Rhombus is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Rhombus?"}
{"completion": " The Latex Code for equation Ellipsoidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "How to write equation Ellipsoid?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>r</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Area of a Parallelogramis <equation>A = bh</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Parallelogram?"}
{"completion": " The Latex Code for equation Elliptic Coneis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Elliptic Cone?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 2D is: Point 1.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Area of a Equilateral Triangle is: <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. Here is the brief introduction of Area of a Equilateral Triangle:\n        Latex code for Area of a Equilateral Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Equilateral Triangle?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>a</equation> in Elliptic Cone is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>a</equation> in Elliptic Cone?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone is: Center Coordinates of Elliptic Cone.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone?"}
{"completion": " The Latex Code for equation Surface area of a Cuboidis <equation>S = 2lw + 2lh + 2wh</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Surface area of a Cuboid?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Cylinder is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>a</equation> in Elliptic Cylinder?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a cylinder is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>\\pi</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>l</equation> in Area of a Rectangle is: Length.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>l</equation> in Area of a Rectangle?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>a</equation> in Spiral of Archimedes is: a.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>a</equation> in Spiral of Archimedes?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Elliptic Cylinder is: Center Coordinates of Elliptic Cylinder.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x_0,y_0)</equation> in Elliptic Cylinder?"}
{"completion": " The Latex Code for equation Cartesian to Cylindrical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Cartesian to Cylindrical Coordinates?"}
{"completion": " The Latex Code for equation Distance Between Two Points 3Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Distance Between Two Points 3D?"}
{"completion": " The Latex Code for equation Planeis <equation>Ax + By + Cz + D = 0</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Plane?"}
{"completion": " The equation for Area of a Parallelogram is: <equation>A = bh</equation>. Here is the brief introduction of Area of a Parallelogram:\n        Latex code for Area of a Parallelogram.\n        \n: Area\n: Length of Base\n: Length of Height of parallelogram\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Parallelogram?"}
{"completion": " The equation for Elliptic Cylinder is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Elliptic Cylinder:\n        Latex code for Elliptic Cylinder.\n        \n: Center Coordinates of Elliptic Cylinder\n: Length of Axis x\n: Length of Axis y\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Elliptic Cylinder?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>c</equation> in Ellipsoid is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>c</equation> in Ellipsoid?"}
{"completion": " The equation for Area of a Regular Polygon is <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Regular Polygon is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Regular Polygon?"}
{"completion": " The Latex Code for equation Circleis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Circle?"}
{"completion": " The equation for Elliptic Cone is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. Here is the brief introduction of Elliptic Cone:\n        Latex code for Elliptic Cone.\n        \n: Center Coordinates of Elliptic Cone\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Elliptic Cone?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>h</equation> in Area of a Parallelogram is: Length of Height of parallelogram.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>h</equation> in Area of a Parallelogram?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Spherical Coordinates:\n        Latex code for Cartesian to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(z1,z2)</equation> in Distance Between Two Points 3D is: Point 3.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(z1,z2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 3D is: Point 1.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x1,x2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The Latex Code for equation Area of a Rectangleis <equation>A = lw</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Rectangle?"}
{"completion": " The Latex Code for equation Distance Between Two Points 3Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Distance Between Two Points 3D?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates is: Cylindrical Coordinates.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>l</equation> in Surface area of a Cuboid is: Length.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>l</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Eccentricity of a Hyperbola is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola is: Eccentricity.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Trapezoid is: Height.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>h</equation> in Area of a Trapezoid?"}
{"completion": " The Latex Code for equation Distance Between Two Points 2Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Distance Between Two Points 2D?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 3D is: Point 2.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(y1,y2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The Latex Code for equation Elliptic Cylinderis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "How to write equation Elliptic Cylinder?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Circle is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Circle?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Trapezoid is: Height.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>h</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Area of a Trapezoid is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Trapezoid:\n        Latex code for Area of a Trapezoid.\n        \n: Area\n: Length of top of trapezoid\n: Length of bottom of trapezoid\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Trapezoid?"}
{"completion": " The equation for Elliptic Cylinder is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Elliptic Cylinder:\n        Latex code for Elliptic Cylinder.\n        \n: Center Coordinates of Elliptic Cylinder\n: Length of Axis x\n: Length of Axis y\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Elliptic Cylinder?"}
{"completion": " The equation for Surface area of a Sphere is: <equation>S = 4\\\\pi r^2</equation>. Here is the brief introduction of Surface area of a Sphere:\n        Latex code for Surface area of a sphere.\n        \n: Surface\n: Constant of Pi\n: Radius r\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Surface area of a Sphere?"}
{"completion": " The Latex Code for equation Cylindrical to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Cartesian to Polar Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Polar Coordinates:\n        Latex code for Cartesian to Polar Coordinates.\n        \n: Polar Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Cartesian to Polar Coordinates?"}
{"completion": " The Latex Code for equation Eccentricity of an Ellipseis <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Eccentricity of an Ellipse?"}
{"completion": " The Latex Code for equation Area of a Regular Polygonis <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Regular Polygon?"}
{"completion": " The Latex Code for equation Surface area of a cylinderis <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Area of a Squareis <equation>A = x^2</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Square?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>w</equation> in Surface area of a Cuboid is: Width.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>w</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a Sphere is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>\\pi</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 3D is: Point 1.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x1,x2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>w</equation> in Area of a Rectangle is: Width.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>w</equation> in Area of a Rectangle?"}
{"completion": " The Latex Code for equation Distance Between Two Points 3Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Distance Between Two Points 3D?"}
{"completion": " The equation for Sphere is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. Here is the brief introduction of Sphere:\n        Latex code for Parabola.\n        \n: Center Coordinates of Sphere\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Sphere?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone is: Center Coordinates of Elliptic Cone.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone?"}
{"completion": " The Latex Code for equation Eccentricity of an Ellipseis <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Eccentricity of an Ellipse?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>c</equation> in Elliptic Cone is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>c</equation> in Elliptic Cone?"}
{"completion": " The Latex Code for equation Area of a Equilateral Triangleis <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Equilateral Triangle?"}
{"completion": " The Latex Code for equation Cartesian to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Cartesian to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Elliptic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Elliptic Paraboloid?"}
{"completion": " The Latex Code for equation Circleis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Circle?"}
{"completion": " The equation for Area of a Regular Polygon is: <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. Here is the brief introduction of Area of a Regular Polygon:\n        Latex code for Area of a Regular Polygon.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Regular Polygon?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Ellipsoid is: Center Coordinates of Ellipsoid.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Ellipsoid?"}
{"completion": " The equation for Area of a Rhombus is <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Rhombus is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Rhombus?"}
{"completion": " The related materials of Area of a Rectangle is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Rectangle?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Polar Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cylindrical to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a cylinder is: Height.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>h</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Area of a Regular Polygon is <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Regular Polygon is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Regular Polygon?"}
{"completion": " The Latex Code for equation Area of a Trapezoidis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Trapezoid?"}
{"completion": " The Latex Code for equation Area of a Sectoris <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Sector?"}
{"completion": " The Latex Code for equation Eccentricity of an Ellipseis <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Eccentricity of an Ellipse?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cylindrical to Spherical Coordinates:\n        Latex code for Cylindrical to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>w</equation> in Area of a Rectangle is: Width.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>w</equation> in Area of a Rectangle?"}
{"completion": " The related materials of Area of a Parallelogram is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Parallelogram?"}
{"completion": " The equation for Area of a Regular Polygon is: <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. Here is the brief introduction of Area of a Regular Polygon:\n        Latex code for Area of a Regular Polygon.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Regular Polygon?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Surface area of a Sphere is: Radius r.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>r</equation> in Surface area of a Sphere?"}
{"completion": " The Latex Code for equation Cartesian to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Cartesian to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Surface area of a cubeis <equation>S = 6x^2</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Surface area of a cube?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 3D is: Distance.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>d</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a Cuboid is: Height.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>h</equation> in Surface area of a Cuboid?"}
{"completion": " The Latex Code for equation Hyperbolais <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Hyperbola?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>D</equation> in Plane is: Bias.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>D</equation> in Plane?"}
{"completion": " The Latex Code for equation Area of a Rectangleis <equation>A = lw</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Rectangle?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>R</equation> in Circle is: Radius.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>R</equation> in Circle?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cube is: Surface.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>S</equation> in Surface area of a cube?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Trapezoid is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Spherical Coordinates:\n        Latex code for Cartesian to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>a</equation> in Elliptic Cone is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>a</equation> in Elliptic Cone?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid is: Center Point.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>c</equation> in Elliptic Paraboloid is: Length of Axis z.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>c</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Sphere is: Center Coordinates of Sphere.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Sphere?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipsoid is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>a</equation> in Ellipsoid?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a cylinder is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>\\pi</equation> in Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Cartesian to Cylindrical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbola is: Length a.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>a</equation> in Hyperbola?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipse is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>a</equation> in Ellipse?"}
{"completion": " The Latex Code for equation Ellipseis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Ellipse?"}
{"completion": " The equation for Cartesian to Polar Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Polar Coordinates:\n        Latex code for Cartesian to Polar Coordinates.\n        \n: Polar Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Cartesian to Polar Coordinates?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Sphere is: Surface.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>S</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Area of a Parallelogram is: <equation>A = bh</equation>. Here is the brief introduction of Area of a Parallelogram:\n        Latex code for Area of a Parallelogram.\n        \n: Area\n: Length of Base\n: Length of Height of parallelogram\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Parallelogram?"}
{"completion": " The Latex Code for equation Hyperbolais <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Hyperbola?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 2D is: Point 2.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(y1,y2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The related materials of Area of a Trapezoid is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Trapezoid?"}
{"completion": " The Latex Code for equation Area of a Parallelogramis <equation>A = bh</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Parallelogram?"}
{"completion": " The equation for Elliptic Cylinder is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Elliptic Cylinder:\n        Latex code for Elliptic Cylinder.\n        \n: Center Coordinates of Elliptic Cylinder\n: Length of Axis x\n: Length of Axis y\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Elliptic Cylinder?"}
{"completion": " The Latex Code for equation Parabolais <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Parabola?"}
{"completion": " The equation for Plane is: <equation>Ax + By + Cz + D = 0</equation>. Here is the brief introduction of Plane:\n        Latex code for Parabola.\n        \n: Coefficient of x\n: Coefficient of y\n: Coefficient of z\n: Bias\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Plane?"}
{"completion": " The equation for Ellipse is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipse:\n        Latex code for Ellipse.\n        \n: Center Coordinates of Ellipse\n: Length of Axis a\n: Length of Axis b\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Ellipse?"}
{"completion": " The Latex Code for equation Surface area of a cubeis <equation>S = 6x^2</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Surface area of a cube?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_2</equation> in Area of a Trapezoid is: Length of bottom of trapezoid.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>x_2</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Elliptic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Elliptic Paraboloid:\n        Latex code for Elliptic Paraboloid.\n        \n: Center Coordinates of Elliptic Paraboloid.\n: Length of Axis x\n: Length of Axis y\n: Length of Axis z\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Elliptic Paraboloid?"}
{"completion": " The equation for Parabola is: <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>. Here is the brief introduction of Parabola:\n        Latex code for Parabola.\n        \n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Parabola?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid is: Center Coordinates of Elliptic Paraboloid..", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid?"}
{"completion": " The Latex Code for equation Cartesian to Polar Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Cartesian to Polar Coordinates?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Ellipsoid is: Center Coordinates of Ellipsoid.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x_0,y_0,z_0)</equation> in Ellipsoid?"}
{"completion": " The equation for Area of a Equilateral Triangle is: <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. Here is the brief introduction of Area of a Equilateral Triangle:\n        Latex code for Area of a Equilateral Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Equilateral Triangle?"}
{"completion": " The equation for Cartesian to Polar Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Polar Coordinates:\n        Latex code for Cartesian to Polar Coordinates.\n        \n: Polar Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Cartesian to Polar Coordinates?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>a</equation> in Elliptic Cone is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>a</equation> in Elliptic Cone?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>C</equation> in Plane is: Coefficient of z.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>C</equation> in Plane?"}
{"completion": " The Latex Code for equation Elliptic Cylinderis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Elliptic Cylinder?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(z1,z2)</equation> in Distance Between Two Points 3D is: Point 3.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(z1,z2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Area of a Sector is: <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. Here is the brief introduction of Area of a Sector:\n        Latex code for Area of a Sector.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Sector?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>\\phi</equation> in Area of a Circle is: Constant ranging from 3.1415926-3.1415927.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>\\phi</equation> in Area of a Circle?"}
{"completion": " The Latex Code for equation Elliptic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Elliptic Paraboloid?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Triangle is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Triangle?"}
{"completion": " The Latex Code for equation Spiral of Archimedesis <equation>r = a \\\\theta</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Spiral of Archimedes?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>r</equation> in Spiral of Archimedes is: r.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>r</equation> in Spiral of Archimedes?"}
{"completion": " The equation for Elliptic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Elliptic Paraboloid:\n        Latex code for Elliptic Paraboloid.\n        \n: Center Coordinates of Elliptic Paraboloid.\n: Length of Axis x\n: Length of Axis y\n: Length of Axis z\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Elliptic Paraboloid?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Sphere is: Center Coordinates of Sphere.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x_0,y_0,z_0)</equation> in Sphere?"}
{"completion": " The Latex Code for equation Sphereis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>", "tag": "Math,Geometry", "prompt": "How to write equation Sphere?"}
{"completion": " The Latex Code for equation Area of a Rhombusis <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Rhombus?"}
{"completion": " The equation for Circle is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. Here is the brief introduction of Circle:\n        Latex code for Circle\n        \n: Coordinates of Circle Center\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Circle?"}
{"completion": " The Latex Code for equation Area of a Rhombusis <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Rhombus?"}
{"completion": " The Latex Code for equation Area of a Sectoris <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Sector?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>l</equation> in Area of a Rectangle is: Length.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>l</equation> in Area of a Rectangle?"}
{"completion": " The equation for Ellipse is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipse:\n        Latex code for Ellipse.\n        \n: Center Coordinates of Ellipse\n: Length of Axis a\n: Length of Axis b\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Ellipse?"}
{"completion": " The equation for Ellipsoid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipsoid:\n        Latex code for Ellipsoid.\n        \n: Center Coordinates of Ellipsoid\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Ellipsoid?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cube is: Surface.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>S</equation> in Surface area of a cube?"}
{"completion": " The equation for Surface area of a cylinder is: <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. Here is the brief introduction of Surface area of a cylinder:\n        Latex code for Surface area of a cylinder.\n        \n: Surface\n: Constant of Pi\n: Radius r\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Area of a Equilateral Triangleis <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Equilateral Triangle?"}
{"completion": " The equation for Hyperbola is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Hyperbola:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Hyperbola?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>R</equation> in Circle is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>R</equation> in Circle?"}
{"completion": " The equation for Area of a Regular Polygon is: <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. Here is the brief introduction of Area of a Regular Polygon:\n        Latex code for Area of a Regular Polygon.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Regular Polygon?"}
{"completion": " The equation for Area of a Triangle is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Triangle:\n        Latex code for Area of a Triangle.\n        \n: Area\n: Length of Bottom of Triangle\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Triangle?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a Sphere is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>\\pi</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Paraboloid is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>a</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Circle is: Coordinates of Circle Center.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x_0,y_0)</equation> in Circle?"}
{"completion": " The Latex Code for equation Spiral of Archimedesis <equation>r = a \\\\theta</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Spiral of Archimedes?"}
{"completion": " The equation for Area of a Regular Polygon is: <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. Here is the brief introduction of Area of a Regular Polygon:\n        Latex code for Area of a Regular Polygon.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Regular Polygon?"}
{"completion": " The equation for Area of a Sector is <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Sector is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Sector?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Ellipse is: Center Coordinates of Ellipse.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x_0,y_0)</equation> in Ellipse?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid is: Center Coordinates of Elliptic Paraboloid..", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid?"}
{"completion": " The Latex Code for equation Area of a Squareis <equation>A = x^2</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Square?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Polar Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>r</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The Latex Code for equation Elliptic Coneis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Elliptic Cone?"}
{"completion": " The equation for Eccentricity of a Hyperbola is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of a Hyperbola:\n        Latex code for Eccentricity of a Hyperbola.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Eccentricity of a Hyperbola?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>b</equation> in Area of a Triangle is: Length of Bottom of Triangle.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>b</equation> in Area of a Triangle?"}
{"completion": " The equation for Area of a Ellipse is <equation>A = \\\\pi r_1 r_2</equation>. The meaning of symbol <equation>A</equation> in Area of a Ellipse is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Ellipse?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Circle is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Circle?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Triangle is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Triangle?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>c</equation> in Elliptic Cone is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>c</equation> in Elliptic Cone?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Sphere is: Center Coordinates of Sphere.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x_0,y_0,z_0)</equation> in Sphere?"}
{"completion": " The Latex Code for equation Elliptic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Elliptic Paraboloid?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>c</equation> in Ellipsoid is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>c</equation> in Ellipsoid?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipse is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>b</equation> in Ellipse?"}
{"completion": " The equation for Hyperbolic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Hyperbolic Paraboloid:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Hyperbolic Paraboloid?"}
{"completion": " The equation for Area of a Rectangle is: <equation>A = lw</equation>. Here is the brief introduction of Area of a Rectangle:\n        Latex code for Area of a Rectangle.\n        \n: Area\n: Width\n: Length\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Rectangle?"}
{"completion": " The Latex Code for equation Surface area of a cubeis <equation>S = 6x^2</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Surface area of a cube?"}
{"completion": " The equation for Area of a Triangle is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Triangle:\n        Latex code for Area of a Triangle.\n        \n: Area\n: Length of Bottom of Triangle\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Triangle?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>c</equation> in Elliptic Paraboloid is: Length of Axis z.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>c</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Area of a Sector is: <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. Here is the brief introduction of Area of a Sector:\n        Latex code for Area of a Sector.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Sector?"}
{"completion": " The Latex Code for equation Area of a Trapezoidis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Trapezoid?"}
{"completion": " The equation for Area of a Equilateral Triangle is <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. The meaning of symbol <equation>A</equation> in Area of a Equilateral Triangle is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Equilateral Triangle?"}
{"completion": " The equation for Hyperbola is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Hyperbola:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Hyperbola?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_1</equation> in Area of a Trapezoid is: Length of top of trapezoid.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>x_1</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cylindrical to Spherical Coordinates:\n        Latex code for Cylindrical to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Cylindrical to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Area of a Regular Polygonis <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Regular Polygon?"}
{"completion": " The Latex Code for equation Area of a Triangleis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Triangle?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a Sphere is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>\\pi</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Elliptic Cone is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. Here is the brief introduction of Elliptic Cone:\n        Latex code for Elliptic Cone.\n        \n: Center Coordinates of Elliptic Cone\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Elliptic Cone?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>\\phi</equation> in Area of a Circle is: Constant ranging from 3.1415926-3.1415927.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>\\phi</equation> in Area of a Circle?"}
{"completion": " The equation for Area of a Ellipse is: <equation>A = \\\\pi r_1 r_2</equation>. Here is the brief introduction of Area of a Ellipse:\n        Latex code for Area of a Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Ellipse?"}
{"completion": " The Latex Code for equation Cylindrical to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Cylindrical to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Ellipseis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Ellipse?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbolic Paraboloid is: Length a.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>a</equation> in Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Cartesian to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Ellipse is: Center Coordinates of Ellipse.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x_0,y_0)</equation> in Ellipse?"}
{"completion": " The Latex Code for equation Spiral of Archimedesis <equation>r = a \\\\theta</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Spiral of Archimedes?"}
{"completion": " The related materials of Surface area of a cylinder is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Surface area of a cylinder?"}
{"completion": " The equation for Elliptic Cylinder is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Elliptic Cylinder:\n        Latex code for Elliptic Cylinder.\n        \n: Center Coordinates of Elliptic Cylinder\n: Length of Axis x\n: Length of Axis y\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Elliptic Cylinder?"}
{"completion": " The Latex Code for equation Area of a Circleis <equation>A = \\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Circle?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>R</equation> in Circle is: Radius.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>R</equation> in Circle?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>w</equation> in Surface area of a Cuboid is: Width.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>w</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>w</equation> in Area of a Rectangle is: Width.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>w</equation> in Area of a Rectangle?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>\\theta</equation> in Spiral of Archimedes is: Angle Theta.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>\\theta</equation> in Spiral of Archimedes?"}
{"completion": " The Latex Code for equation Area of a Ellipseis <equation>A = \\\\pi r_1 r_2</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Ellipse?"}
{"completion": " The equation for Area of a Parallelogram is: <equation>A = bh</equation>. Here is the brief introduction of Area of a Parallelogram:\n        Latex code for Area of a Parallelogram.\n        \n: Area\n: Length of Base\n: Length of Height of parallelogram\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Parallelogram?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>B</equation> in Plane is: Coefficient of y.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>B</equation> in Plane?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Trapezoid is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Trapezoid?"}
{"completion": " The Latex Code for equation Hyperbolic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Hyperbolic Paraboloid?"}
{"completion": " The equation for Area of a Square is: <equation>A = x^2</equation>. Here is the brief introduction of Area of a Square:\n        Latex code for Area of a Square.\n        \n: Area\n: Length/Width of Square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Square?"}
{"completion": " The related materials of Area of a Square is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Square?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>A</equation> in Plane is: Coefficient of x.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Plane?"}
{"completion": " The Latex Code for equation Ellipsoidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Ellipsoid?"}
{"completion": " The Latex Code for equation Area of a Trapezoidis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Trapezoid?"}
{"completion": " The equation for Plane is: <equation>Ax + By + Cz + D = 0</equation>. Here is the brief introduction of Plane:\n        Latex code for Parabola.\n        \n: Coefficient of x\n: Coefficient of y\n: Coefficient of z\n: Bias\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Plane?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Cylindrical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>r</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The Latex Code for equation Ellipseis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Ellipse?"}
{"completion": " The Latex Code for equation Eccentricity of an Ellipseis <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Eccentricity of an Ellipse?"}
{"completion": " The Latex Code for equation Ellipseis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Ellipse?"}
{"completion": " The Latex Code for equation Elliptic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Elliptic Paraboloid?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Sphere is: Surface.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>S</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Cuboid is: Surface.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>S</equation> in Surface area of a Cuboid?"}
{"completion": " The Latex Code for equation Parabolais <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Parabola?"}
{"completion": " The Latex Code for equation Cartesian to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Cartesian to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Area of a Trapezoidis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Trapezoid?"}
{"completion": " The equation for Surface area of a Sphere is: <equation>S = 4\\\\pi r^2</equation>. Here is the brief introduction of Surface area of a Sphere:\n        Latex code for Surface area of a sphere.\n        \n: Surface\n: Constant of Pi\n: Radius r\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Surface area of a Sphere?"}
{"completion": " The related materials of Ellipse is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Ellipse?"}
{"completion": " The equation for Surface area of a cylinder is: <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. Here is the brief introduction of Surface area of a cylinder:\n        Latex code for Surface area of a cylinder.\n        \n: Surface\n: Constant of Pi\n: Radius r\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Surface area of a cylinder?"}
{"completion": " The equation for Area of a Circle is: <equation>A = \\\\pi r^2</equation>. Here is the brief introduction of Area of a Circle:\n        Latex code for Area of a Circle.\n        \n: Area\n: Constant ranging from 3.1415926-3.1415927\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Circle?"}
{"completion": " The Latex Code for equation Surface area of a Sphereis <equation>S = 4\\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Surface area of a Sphere?"}
{"completion": " The equation for Distance Between Two Points 2D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 2D:\n        Latex code for Distance Between Two Points 2D.\n        \n: Distance\n: Point 1\n: Point 2\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Distance Between Two Points 2D?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_2</equation> in Area of a Trapezoid is: Length of bottom of trapezoid.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>x_2</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a Sphere is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>\\pi</equation> in Surface area of a Sphere?"}
{"completion": " The Latex Code for equation Eccentricity of a Hyperbolais <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Eccentricity of a Hyperbola?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>b</equation> in Area of a Parallelogram is: Length of Base.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>b</equation> in Area of a Parallelogram?"}
{"completion": " The Latex Code for equation Area of a Sectoris <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Sector?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cylindrical to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>r</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Surface area of a Cuboid is: <equation>S = 2lw + 2lh + 2wh</equation>. Here is the brief introduction of Surface area of a Cuboid:\n        Latex code for Surface area of a cuboid.\n        \n: Surface\n: Length\n: Width\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Surface area of a Cuboid?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cube is: Surface.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>S</equation> in Surface area of a cube?"}
{"completion": " The Latex Code for equation Surface area of a Cuboidis <equation>S = 2lw + 2lh + 2wh</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Surface area of a Cuboid?"}
{"completion": " The Latex Code for equation Eccentricity of a Hyperbolais <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Eccentricity of a Hyperbola?"}
{"completion": " The Latex Code for equation Circleis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Circle?"}
{"completion": " The related materials of Ellipsoid is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Ellipsoid?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone is: Center Coordinates of Elliptic Cone.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Cylinder is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>b</equation> in Elliptic Cylinder?"}
{"completion": " The equation for Area of a Triangle is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Triangle:\n        Latex code for Area of a Triangle.\n        \n: Area\n: Length of Bottom of Triangle\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Triangle?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>r</equation> in Surface area of a cylinder is: Radius r.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>r</equation> in Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Surface area of a cubeis <equation>S = 6x^2</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Surface area of a cube?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Sphere is: Surface.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>S</equation> in Surface area of a Sphere?"}
{"completion": " The Latex Code for equation Cylindrical to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>r</equation> in Spiral of Archimedes is: r.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>r</equation> in Spiral of Archimedes?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Paraboloid is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>b</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Area of a Trapezoid is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Trapezoid:\n        Latex code for Area of a Trapezoid.\n        \n: Area\n: Length of top of trapezoid\n: Length of bottom of trapezoid\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Trapezoid?"}
{"completion": " The related materials of Cartesian to Spherical Coordinates is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Elliptic Cylinder is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Elliptic Cylinder:\n        Latex code for Elliptic Cylinder.\n        \n: Center Coordinates of Elliptic Cylinder\n: Length of Axis x\n: Length of Axis y\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Elliptic Cylinder?"}
{"completion": " The equation for Spiral of Archimedes is: <equation>r = a \\\\theta</equation>. Here is the brief introduction of Spiral of Archimedes:\n        Latex code for Spiral of Archimedes.\n        \n: r\n: a\n: Angle Theta\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Spiral of Archimedes?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 2D is: Distance.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>d</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Ellipsoid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipsoid:\n        Latex code for Ellipsoid.\n        \n: Center Coordinates of Ellipsoid\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Ellipsoid?"}
{"completion": " The equation for Surface area of a cube is: <equation>S = 6x^2</equation>. Here is the brief introduction of Surface area of a cube:\n        Latex code for Surface area of a cube.\n        \n: Surface\n: Length of a square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Surface area of a cube?"}
{"completion": " The equation for Area of a Ellipse is: <equation>A = \\\\pi r_1 r_2</equation>. Here is the brief introduction of Area of a Ellipse:\n        Latex code for Area of a Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Ellipse?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>R</equation> in Sphere is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>R</equation> in Sphere?"}
{"completion": " The related materials of Eccentricity of a Hyperbola is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Eccentricity of a Hyperbola?"}
{"completion": " The Latex Code for equation Hyperbolic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Hyperbolic Paraboloid?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>w</equation> in Surface area of a Cuboid is: Width.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>w</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid is: Center Coordinates of Elliptic Paraboloid..", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 3D is: Point 1.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x1,x2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The Latex Code for equation Area of a Squareis <equation>A = x^2</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Square?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid is: Center Point.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Cylindrical Coordinates:\n        Latex code for Cartesian to Cylindrical Coordinates.\n        \n: Cylindrical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Cartesian to Cylindrical Coordinates?"}
{"completion": " The Latex Code for equation Area of a Sectoris <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Sector?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y)</equation> in Cartesian to Polar Coordinates is: Polar Coordinates.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x,y)</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Cylinder is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>a</equation> in Elliptic Cylinder?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbola is: Length b.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>b</equation> in Hyperbola?"}
{"completion": " The related materials of Area of a Sector is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Sector?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Trapezoid is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipsoid is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>a</equation> in Ellipsoid?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbola is: Center Point.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x_0,y_0)</equation> in Hyperbola?"}
{"completion": " The Latex Code for equation Area of a Circleis <equation>A = \\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Circle?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Circle is: Coordinates of Circle Center.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x_0,y_0)</equation> in Circle?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a Cuboid is: Height.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>h</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a Cuboid is: Height.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>h</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Plane is: <equation>Ax + By + Cz + D = 0</equation>. Here is the brief introduction of Plane:\n        Latex code for Parabola.\n        \n: Coefficient of x\n: Coefficient of y\n: Coefficient of z\n: Bias\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Plane?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipsoid is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>a</equation> in Ellipsoid?"}
{"completion": " The Latex Code for equation Distance Between Two Points 2Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Distance Between Two Points 2D?"}
{"completion": " The equation for Area of a Regular Polygon is: <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. Here is the brief introduction of Area of a Regular Polygon:\n        Latex code for Area of a Regular Polygon.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Regular Polygon?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Cylindrical Coordinates:\n        Latex code for Cartesian to Cylindrical Coordinates.\n        \n: Cylindrical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Sphere is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. Here is the brief introduction of Sphere:\n        Latex code for Parabola.\n        \n: Center Coordinates of Sphere\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Sphere?"}
{"completion": " The related materials of Eccentricity of an Ellipse is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Eccentricity of an Ellipse?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipse is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>a</equation> in Ellipse?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipse is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>b</equation> in Ellipse?"}
{"completion": " The equation for Area of a Rhombus is: <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. Here is the brief introduction of Area of a Rhombus:\n        Latex code for Area of a Rhombus.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Rhombus?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Triangle is: Height.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>h</equation> in Area of a Triangle?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>\\phi</equation> in Area of a Circle is: Constant ranging from 3.1415926-3.1415927.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>\\phi</equation> in Area of a Circle?"}
{"completion": " The related materials of Distance Between Two Points 2D is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Distance Between Two Points 2D?"}
{"completion": " The equation for Surface area of a cylinder is: <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. Here is the brief introduction of Surface area of a cylinder:\n        Latex code for Surface area of a cylinder.\n        \n: Surface\n: Constant of Pi\n: Radius r\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Surface area of a cylinder?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Triangle is: Height.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>h</equation> in Area of a Triangle?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Ellipsoid is: Center Coordinates of Ellipsoid.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x_0,y_0,z_0)</equation> in Ellipsoid?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Elliptic Cylinder is: Center Coordinates of Elliptic Cylinder.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x_0,y_0)</equation> in Elliptic Cylinder?"}
{"completion": " The related materials of Circle is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Circle?"}
{"completion": " The equation for Area of a Circle is: <equation>A = \\\\pi r^2</equation>. Here is the brief introduction of Area of a Circle:\n        Latex code for Area of a Circle.\n        \n: Area\n: Constant ranging from 3.1415926-3.1415927\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Circle?"}
{"completion": " The Latex Code for equation Area of a Regular Polygonis <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Regular Polygon?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>w</equation> in Area of a Rectangle is: Width.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>w</equation> in Area of a Rectangle?"}
{"completion": " The related materials of Surface area of a Cuboid is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Surface area of a Cuboid?"}
{"completion": " The Latex Code for equation Cartesian to Polar Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Cartesian to Polar Coordinates?"}
{"completion": " The equation for Ellipsoid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipsoid:\n        Latex code for Ellipsoid.\n        \n: Center Coordinates of Ellipsoid\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Ellipsoid?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Cylindrical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>r</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The Latex Code for equation Ellipseis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Ellipse?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Ellipse is: Center Coordinates of Ellipse.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x_0,y_0)</equation> in Ellipse?"}
{"completion": " The Latex Code for equation Area of a Regular Polygonis <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Regular Polygon?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbola is: Center Point.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x_0,y_0)</equation> in Hyperbola?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>D</equation> in Plane is: Bias.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>D</equation> in Plane?"}
{"completion": " The equation for Eccentricity of a Hyperbola is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola is: Eccentricity.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola?"}
{"completion": " The Latex Code for equation Area of a Triangleis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Triangle?"}
{"completion": " The equation for Area of a Equilateral Triangle is <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. The meaning of symbol <equation>A</equation> in Area of a Equilateral Triangle is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Equilateral Triangle?"}
{"completion": " The Latex Code for equation Surface area of a Sphereis <equation>S = 4\\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Surface area of a Sphere?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a cylinder is: Height.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>h</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Area of a Ellipse is: <equation>A = \\\\pi r_1 r_2</equation>. Here is the brief introduction of Area of a Ellipse:\n        Latex code for Area of a Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Ellipse?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipse is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>b</equation> in Ellipse?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Cylinder is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>a</equation> in Elliptic Cylinder?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(z1,z2)</equation> in Distance Between Two Points 3D is: Point 3.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(z1,z2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>A</equation> in Area of a Parallelogram is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Parallelogram?"}
{"completion": " The Latex Code for equation Planeis <equation>Ax + By + Cz + D = 0</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Plane?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cylinder is: Surface.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>S</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Surface area of a Sphere is: <equation>S = 4\\\\pi r^2</equation>. Here is the brief introduction of Surface area of a Sphere:\n        Latex code for Surface area of a sphere.\n        \n: Surface\n: Constant of Pi\n: Radius r\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Surface area of a Sphere?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Cylinder is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>a</equation> in Elliptic Cylinder?"}
{"completion": " The related materials of Area of a Ellipse is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Ellipse?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>A</equation> in Area of a Rectangle is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Rectangle?"}
{"completion": " The equation for Distance Between Two Points 3D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 3D:\n        Latex code for Distance Between Two Points 3D.\n        \n: Distance\n: Point 1\n: Point 2\n: Point 3\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Distance Between Two Points 3D?"}
{"completion": " The equation for Plane is: <equation>Ax + By + Cz + D = 0</equation>. Here is the brief introduction of Plane:\n        Latex code for Parabola.\n        \n: Coefficient of x\n: Coefficient of y\n: Coefficient of z\n: Bias\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Plane?"}
{"completion": " The Latex Code for equation Area of a Regular Polygonis <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Regular Polygon?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Area of a Circle is: Radius.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Area of a Circle?"}
{"completion": " The related materials of Cartesian to Polar Coordinates is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Cartesian to Polar Coordinates?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Paraboloid is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>a</equation> in Elliptic Paraboloid?"}
{"completion": " The Latex Code for equation Cartesian to Cylindrical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Area of a Trapezoid is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Trapezoid:\n        Latex code for Area of a Trapezoid.\n        \n: Area\n: Length of top of trapezoid\n: Length of bottom of trapezoid\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Trapezoid?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbolic Paraboloid is: Length b.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>b</equation> in Hyperbolic Paraboloid?"}
{"completion": " The related materials of Area of a Triangle is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Triangle?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Cylinder is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>b</equation> in Elliptic Cylinder?"}
{"completion": " The Latex Code for equation Area of a Circleis <equation>A = \\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Circle?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Square is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Square?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 2D is: Distance.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>d</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Area of a Regular Polygon is <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Regular Polygon is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Regular Polygon?"}
{"completion": " The equation for Parabola is: <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>. Here is the brief introduction of Parabola:\n        Latex code for Parabola.\n        \n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Parabola?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>l</equation> in Area of a Rectangle is: Length.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>l</equation> in Area of a Rectangle?"}
{"completion": " The related materials of Elliptic Cylinder is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Elliptic Cylinder?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 2D is: Point 1.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x1,x2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The related materials of Area of a Equilateral Triangle is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Equilateral Triangle?"}
{"completion": " The Latex Code for equation Ellipsoidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Ellipsoid?"}
{"completion": " The Latex Code for equation Spiral of Archimedesis <equation>r = a \\\\theta</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Spiral of Archimedes?"}
{"completion": " The equation for Area of a Regular Polygon is <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Regular Polygon is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Regular Polygon?"}
{"completion": " The Latex Code for equation Cylindrical to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Cylindrical to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Elliptic Coneis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Elliptic Cone?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>R</equation> in Sphere is: Radius.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>R</equation> in Sphere?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 3D is: Point 2.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(y1,y2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>r</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Planeis <equation>Ax + By + Cz + D = 0</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Plane?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>l</equation> in Area of a Rectangle is: Length.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>l</equation> in Area of a Rectangle?"}
{"completion": " The Latex Code for equation Area of a Triangleis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Triangle?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Cylinder is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>b</equation> in Elliptic Cylinder?"}
{"completion": " The Latex Code for equation Distance Between Two Points 2Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Distance Between Two Points 2D?"}
{"completion": " The Latex Code for equation Area of a Equilateral Triangleis <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Equilateral Triangle?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>w</equation> in Surface area of a Cuboid is: Width.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>w</equation> in Surface area of a Cuboid?"}
{"completion": " The related materials of Hyperbola is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Hyperbola?"}
{"completion": " The equation for Area of a Rhombus is <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Rhombus is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Rhombus?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone is: Center Coordinates of Elliptic Cone.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipse is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>b</equation> in Ellipse?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipsoid is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>b</equation> in Ellipsoid?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Ellipse is: Center Coordinates of Ellipse.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x_0,y_0)</equation> in Ellipse?"}
{"completion": " The Latex Code for equation Area of a Equilateral Triangleis <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Equilateral Triangle?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>a</equation> in Spiral of Archimedes is: a.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>a</equation> in Spiral of Archimedes?"}
{"completion": " The equation for Area of a Ellipse is: <equation>A = \\\\pi r_1 r_2</equation>. Here is the brief introduction of Area of a Ellipse:\n        Latex code for Area of a Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Ellipse?"}
{"completion": " The Latex Code for equation Distance Between Two Points 2Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Distance Between Two Points 2D?"}
{"completion": " The equation for Area of a Ellipse is <equation>A = \\\\pi r_1 r_2</equation>. The meaning of symbol <equation>A</equation> in Area of a Ellipse is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Ellipse?"}
{"completion": " The Latex Code for equation Distance Between Two Points 2Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Distance Between Two Points 2D?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>x</equation> in Surface area of a cube is: Length of a square.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>x</equation> in Surface area of a cube?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>c</equation> in Elliptic Cone is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>c</equation> in Elliptic Cone?"}
{"completion": " The Latex Code for equation Hyperbolais <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Hyperbola?"}
{"completion": " The equation for Parabola is: <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>. Here is the brief introduction of Parabola:\n        Latex code for Parabola.\n        \n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Parabola?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x,y,z)</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>B</equation> in Plane is: Coefficient of y.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>B</equation> in Plane?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>\\theta</equation> in Spiral of Archimedes is: Angle Theta.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>\\theta</equation> in Spiral of Archimedes?"}
{"completion": " The equation for Ellipse is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipse:\n        Latex code for Ellipse.\n        \n: Center Coordinates of Ellipse\n: Length of Axis a\n: Length of Axis b\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Ellipse?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Elliptic Cylinder is: Center Coordinates of Elliptic Cylinder.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x_0,y_0)</equation> in Elliptic Cylinder?"}
{"completion": " The equation for Eccentricity of a Hyperbola is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola is: Eccentricity.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>\\theta</equation> in Spiral of Archimedes is: Angle Theta.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>\\theta</equation> in Spiral of Archimedes?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Triangle is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Triangle?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 3D is: Point 2.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(y1,y2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Paraboloid is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>b</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>A</equation> in Plane is: Coefficient of x.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Plane?"}
{"completion": " The equation for Area of a Rhombus is <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Rhombus is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Rhombus?"}
{"completion": " The equation for Area of a Sector is <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Sector is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Sector?"}
{"completion": " The Latex Code for equation Ellipseis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "How to write equation Ellipse?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Cylindrical Coordinates:\n        Latex code for Cartesian to Cylindrical Coordinates.\n        \n: Cylindrical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y)</equation> in Cartesian to Polar Coordinates is: Polar Coordinates.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x,y)</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 2D is: Distance.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>d</equation> in Distance Between Two Points 2D?"}
{"completion": " The Latex Code for equation Distance Between Two Points 3Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Distance Between Two Points 3D?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Triangle is: Height.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>h</equation> in Area of a Triangle?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Sphere is: Center Coordinates of Sphere.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x_0,y_0,z_0)</equation> in Sphere?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbolic Paraboloid is: Length a.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>a</equation> in Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Cartesian to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid is: Center Point.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Circle is: Coordinates of Circle Center.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x_0,y_0)</equation> in Circle?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>R</equation> in Sphere is: Radius.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>R</equation> in Sphere?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Surface area of a Sphere is: Radius r.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>r</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Paraboloid is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>a</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>\\phi</equation> in Area of a Circle is: Constant ranging from 3.1415926-3.1415927.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>\\phi</equation> in Area of a Circle?"}
{"completion": " The Latex Code for equation Elliptic Cylinderis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Elliptic Cylinder?"}
{"completion": " The Latex Code for equation Surface area of a Cuboidis <equation>S = 2lw + 2lh + 2wh</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Surface area of a Cuboid?"}
{"completion": " The Latex Code for equation Area of a Squareis <equation>A = x^2</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Square?"}
{"completion": " The equation for Surface area of a Sphere is: <equation>S = 4\\\\pi r^2</equation>. Here is the brief introduction of Surface area of a Sphere:\n        Latex code for Surface area of a sphere.\n        \n: Surface\n: Constant of Pi\n: Radius r\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Surface area of a Sphere?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Square is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Square?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbolic Paraboloid is: Length b.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>b</equation> in Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Area of a Ellipseis <equation>A = \\\\pi r_1 r_2</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Ellipse?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Cylindrical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>r</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Eccentricity of a Hyperbola is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of a Hyperbola:\n        Latex code for Eccentricity of a Hyperbola.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Eccentricity of a Hyperbola?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>r</equation> in Spiral of Archimedes is: r.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>r</equation> in Spiral of Archimedes?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbola is: Length b.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>b</equation> in Hyperbola?"}
{"completion": " The equation for Hyperbolic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Hyperbolic Paraboloid:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Circleis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Circle?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>a</equation> in Spiral of Archimedes is: a.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>a</equation> in Spiral of Archimedes?"}
{"completion": " The Latex Code for equation Area of a Circleis <equation>A = \\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Circle?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Polar Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>r</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The Latex Code for equation Area of a Trapezoidis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Trapezoid?"}
{"completion": " The Latex Code for equation Area of a Trapezoidis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Trapezoid?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>c</equation> in Elliptic Paraboloid is: Length of Axis z.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>c</equation> in Elliptic Paraboloid?"}
{"completion": " The Latex Code for equation Surface area of a Cuboidis <equation>S = 2lw + 2lh + 2wh</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Surface area of a Cuboid?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a Cuboid is: Height.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>h</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbola is: Length a.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>a</equation> in Hyperbola?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>x</equation> in Area of a Square is: Length/Width of Square.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>x</equation> in Area of a Square?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Polar Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>r</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The equation for Hyperbolic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Hyperbolic Paraboloid:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Planeis <equation>Ax + By + Cz + D = 0</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Plane?"}
{"completion": " The equation for Area of a Equilateral Triangle is: <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. Here is the brief introduction of Area of a Equilateral Triangle:\n        Latex code for Area of a Equilateral Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Equilateral Triangle?"}
{"completion": " The Latex Code for equation Surface area of a cylinderis <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Surface area of a cylinder?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Ellipse is: Center Coordinates of Ellipse.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x_0,y_0)</equation> in Ellipse?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Elliptic Cylinder is: Center Coordinates of Elliptic Cylinder.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x_0,y_0)</equation> in Elliptic Cylinder?"}
{"completion": " The Latex Code for equation Circleis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Circle?"}
{"completion": " The equation for Area of a Ellipse is <equation>A = \\\\pi r_1 r_2</equation>. The meaning of symbol <equation>A</equation> in Area of a Ellipse is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Ellipse?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>A</equation> in Area of a Rectangle is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Rectangle?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Cylinder is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>b</equation> in Elliptic Cylinder?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>r</equation> in Surface area of a cylinder is: Radius r.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>r</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Sphere is: Surface.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>S</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Cylinder is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>b</equation> in Elliptic Cylinder?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Elliptic Cone is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. Here is the brief introduction of Elliptic Cone:\n        Latex code for Elliptic Cone.\n        \n: Center Coordinates of Elliptic Cone\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Elliptic Cone?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a cylinder is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>\\pi</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>x</equation> in Area of a Square is: Length/Width of Square.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>x</equation> in Area of a Square?"}
{"completion": " The related materials of Surface area of a cube is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Surface area of a cube?"}
{"completion": " The Latex Code for equation Surface area of a Sphereis <equation>S = 4\\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Surface area of a Sphere?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbolic Paraboloid is: Length b.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>b</equation> in Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Eccentricity of an Ellipseis <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Eccentricity of an Ellipse?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>x</equation> in Surface area of a cube is: Length of a square.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>x</equation> in Surface area of a cube?"}
{"completion": " The equation for Area of a Trapezoid is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Trapezoid:\n        Latex code for Area of a Trapezoid.\n        \n: Area\n: Length of top of trapezoid\n: Length of bottom of trapezoid\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Trapezoid?"}
{"completion": " The Latex Code for equation Area of a Squareis <equation>A = x^2</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Square?"}
{"completion": " The equation for Area of a Rectangle is: <equation>A = lw</equation>. Here is the brief introduction of Area of a Rectangle:\n        Latex code for Area of a Rectangle.\n        \n: Area\n: Width\n: Length\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Rectangle?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cylindrical to Spherical Coordinates:\n        Latex code for Cylindrical to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>A</equation> in Area of a Rectangle is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Rectangle?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cylindrical to Spherical Coordinates:\n        Latex code for Cylindrical to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Cylindrical to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Surface area of a Sphereis <equation>S = 4\\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Surface area of a Sphere?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>A</equation> in Area of a Parallelogram is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Parallelogram?"}
{"completion": " The equation for Ellipse is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipse:\n        Latex code for Ellipse.\n        \n: Center Coordinates of Ellipse\n: Length of Axis a\n: Length of Axis b\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Ellipse?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbolic Paraboloid is: Length a.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>a</equation> in Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Area of a Regular Polygonis <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Regular Polygon?"}
{"completion": " The equation for Elliptic Cone is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. Here is the brief introduction of Elliptic Cone:\n        Latex code for Elliptic Cone.\n        \n: Center Coordinates of Elliptic Cone\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Elliptic Cone?"}
{"completion": " The Latex Code for equation Cartesian to Polar Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Cartesian to Polar Coordinates?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Trapezoid is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Trapezoid?"}
{"completion": " The Latex Code for equation Sphereis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Sphere?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipsoid is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>b</equation> in Ellipsoid?"}
{"completion": " The equation for Surface area of a Cuboid is: <equation>S = 2lw + 2lh + 2wh</equation>. Here is the brief introduction of Surface area of a Cuboid:\n        Latex code for Surface area of a cuboid.\n        \n: Surface\n: Length\n: Width\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Surface area of a Cuboid?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid is: Center Coordinates of Elliptic Paraboloid..", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Area of a Equilateral Triangle is: <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. Here is the brief introduction of Area of a Equilateral Triangle:\n        Latex code for Area of a Equilateral Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Equilateral Triangle?"}
{"completion": " The equation for Surface area of a cylinder is: <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. Here is the brief introduction of Surface area of a cylinder:\n        Latex code for Surface area of a cylinder.\n        \n: Surface\n: Constant of Pi\n: Radius r\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Area of a Rectangleis <equation>A = lw</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Rectangle?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>h</equation> in Area of a Parallelogram is: Length of Height of parallelogram.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>h</equation> in Area of a Parallelogram?"}
{"completion": " The Latex Code for equation Surface area of a Sphereis <equation>S = 4\\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Surface area of a Sphere?"}
{"completion": " The Latex Code for equation Surface area of a Cuboidis <equation>S = 2lw + 2lh + 2wh</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Surface area of a Cuboid?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>a</equation> in Spiral of Archimedes is: a.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>a</equation> in Spiral of Archimedes?"}
{"completion": " The Latex Code for equation Cartesian to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_2</equation> in Area of a Trapezoid is: Length of bottom of trapezoid.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>x_2</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 2D is: Point 2.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(y1,y2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Eccentricity of a Hyperbola is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola is: Eccentricity.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 2D is: Point 1.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x1,x2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>C</equation> in Plane is: Coefficient of z.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>C</equation> in Plane?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>b</equation> in Area of a Triangle is: Length of Bottom of Triangle.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>b</equation> in Area of a Triangle?"}
{"completion": " The Latex Code for equation Area of a Ellipseis <equation>A = \\\\pi r_1 r_2</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Ellipse?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipse is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>a</equation> in Ellipse?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Cylindrical Coordinates:\n        Latex code for Cartesian to Cylindrical Coordinates.\n        \n: Cylindrical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_1</equation> in Area of a Trapezoid is: Length of top of trapezoid.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>x_1</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Parabola is: <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>. Here is the brief introduction of Parabola:\n        Latex code for Parabola.\n        \n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Parabola?"}
{"completion": " The Latex Code for equation Area of a Parallelogramis <equation>A = bh</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Parallelogram?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 3D is: Distance.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>d</equation> in Distance Between Two Points 3D?"}
{"completion": " The Latex Code for equation Area of a Rhombusis <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Rhombus?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a cylinder is: Height.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>h</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipsoid is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>b</equation> in Ellipsoid?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Trapezoid is: Height.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>h</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates is: Cylindrical Coordinates.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>c</equation> in Ellipsoid is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>c</equation> in Ellipsoid?"}
{"completion": " The Latex Code for equation Elliptic Cylinderis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Elliptic Cylinder?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>c</equation> in Elliptic Cone is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>c</equation> in Elliptic Cone?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Sphere is: Surface.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>S</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>x</equation> in Surface area of a cube is: Length of a square.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>x</equation> in Surface area of a cube?"}
{"completion": " The Latex Code for equation Cartesian to Cylindrical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Trapezoid is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Trapezoid?"}
{"completion": " The Latex Code for equation Area of a Parallelogramis <equation>A = bh</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Parallelogram?"}
{"completion": " The equation for Circle is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. Here is the brief introduction of Circle:\n        Latex code for Circle\n        \n: Coordinates of Circle Center\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Circle?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y)</equation> in Cartesian to Polar Coordinates is: Polar Coordinates.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x,y)</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The equation for Area of a Equilateral Triangle is <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. The meaning of symbol <equation>A</equation> in Area of a Equilateral Triangle is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Equilateral Triangle?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cylinder is: Surface.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>S</equation> in Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Planeis <equation>Ax + By + Cz + D = 0</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Plane?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Paraboloid is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>b</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a cylinder is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>\\pi</equation> in Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Area of a Rhombusis <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Area of a Rhombus?"}
{"completion": " The equation for Distance Between Two Points 3D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 3D:\n        Latex code for Distance Between Two Points 3D.\n        \n: Distance\n: Point 1\n: Point 2\n: Point 3\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Distance Between Two Points 3D?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipse is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>b</equation> in Ellipse?"}
{"completion": " The equation for Sphere is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. Here is the brief introduction of Sphere:\n        Latex code for Parabola.\n        \n: Center Coordinates of Sphere\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Sphere?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid is: Center Point.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Area of a Squareis <equation>A = x^2</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Square?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>A</equation> in Plane is: Coefficient of x.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Plane?"}
{"completion": " The equation for Area of a Rhombus is: <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. Here is the brief introduction of Area of a Rhombus:\n        Latex code for Area of a Rhombus.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Rhombus?"}
{"completion": " The equation for Circle is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. Here is the brief introduction of Circle:\n        Latex code for Circle\n        \n: Coordinates of Circle Center\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Circle?"}
{"completion": " The Latex Code for equation Circleis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Circle?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>R</equation> in Circle is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>R</equation> in Circle?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipsoid is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>b</equation> in Ellipsoid?"}
{"completion": " The Latex Code for equation Surface area of a cylinderis <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Planeis <equation>Ax + By + Cz + D = 0</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Plane?"}
{"completion": " The equation for Area of a Parallelogram is: <equation>A = bh</equation>. Here is the brief introduction of Area of a Parallelogram:\n        Latex code for Area of a Parallelogram.\n        \n: Area\n: Length of Base\n: Length of Height of parallelogram\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Parallelogram?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>c</equation> in Ellipsoid is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>c</equation> in Ellipsoid?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>R</equation> in Sphere is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>R</equation> in Sphere?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 3D is: Distance.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>d</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>x</equation> in Surface area of a cube is: Length of a square.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>x</equation> in Surface area of a cube?"}
{"completion": " The related materials of Cylindrical to Spherical Coordinates is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Eccentricity of a Hyperbola is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of a Hyperbola:\n        Latex code for Eccentricity of a Hyperbola.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Eccentricity of a Hyperbola?"}
{"completion": " The equation for Surface area of a Sphere is: <equation>S = 4\\\\pi r^2</equation>. Here is the brief introduction of Surface area of a Sphere:\n        Latex code for Surface area of a sphere.\n        \n: Surface\n: Constant of Pi\n: Radius r\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Surface area of a Sphere?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Ellipsoid is: Center Coordinates of Ellipsoid.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x_0,y_0,z_0)</equation> in Ellipsoid?"}
{"completion": " The equation for Eccentricity of an Ellipse is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of an Ellipse is: Eccentricity.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>\\varepsilon</equation> in Eccentricity of an Ellipse?"}
{"completion": " The equation for Area of a Ellipse is <equation>A = \\\\pi r_1 r_2</equation>. The meaning of symbol <equation>A</equation> in Area of a Ellipse is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Ellipse?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>l</equation> in Surface area of a Cuboid is: Length.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>l</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Spiral of Archimedes is: <equation>r = a \\\\theta</equation>. Here is the brief introduction of Spiral of Archimedes:\n        Latex code for Spiral of Archimedes.\n        \n: r\n: a\n: Angle Theta\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Spiral of Archimedes?"}
{"completion": " The equation for Area of a Sector is: <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. Here is the brief introduction of Area of a Sector:\n        Latex code for Area of a Sector.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Sector?"}
{"completion": " The Latex Code for equation Elliptic Cylinderis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Elliptic Cylinder?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Cuboid is: Surface.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>S</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(z1,z2)</equation> in Distance Between Two Points 3D is: Point 3.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(z1,z2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Surface area of a Cuboid is: <equation>S = 2lw + 2lh + 2wh</equation>. Here is the brief introduction of Surface area of a Cuboid:\n        Latex code for Surface area of a cuboid.\n        \n: Surface\n: Length\n: Width\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Surface area of a Cuboid?"}
{"completion": " The equation for Sphere is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. Here is the brief introduction of Sphere:\n        Latex code for Parabola.\n        \n: Center Coordinates of Sphere\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Sphere?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Elliptic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Elliptic Paraboloid:\n        Latex code for Elliptic Paraboloid.\n        \n: Center Coordinates of Elliptic Paraboloid.\n: Length of Axis x\n: Length of Axis y\n: Length of Axis z\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Elliptic Paraboloid?"}
{"completion": " The equation for Eccentricity of an Ellipse is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of an Ellipse:\n        Latex code for Eccentricity of an Ellipse.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Eccentricity of an Ellipse?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Sphere is: Center Coordinates of Sphere.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x_0,y_0,z_0)</equation> in Sphere?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>b</equation> in Area of a Parallelogram is: Length of Base.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>b</equation> in Area of a Parallelogram?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cylinder is: Surface.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>S</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>A</equation> in Area of a Parallelogram is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Parallelogram?"}
{"completion": " The Latex Code for equation Hyperbolais <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Hyperbola?"}
{"completion": " The Latex Code for equation Hyperbolic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Area of a Parallelogramis <equation>A = bh</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Parallelogram?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Paraboloid is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>b</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbola is: Center Point.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbola?"}
{"completion": " The equation for Hyperbola is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Hyperbola:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Hyperbola?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Surface area of a Sphere is: Radius r.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>r</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Surface area of a cube is: <equation>S = 6x^2</equation>. Here is the brief introduction of Surface area of a cube:\n        Latex code for Surface area of a cube.\n        \n: Surface\n: Length of a square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Surface area of a cube?"}
{"completion": " The equation for Surface area of a cube is: <equation>S = 6x^2</equation>. Here is the brief introduction of Surface area of a cube:\n        Latex code for Surface area of a cube.\n        \n: Surface\n: Length of a square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Surface area of a cube?"}
{"completion": " The Latex Code for equation Surface area of a cubeis <equation>S = 6x^2</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Surface area of a cube?"}
{"completion": " The equation for Distance Between Two Points 2D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 2D:\n        Latex code for Distance Between Two Points 2D.\n        \n: Distance\n: Point 1\n: Point 2\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Distance Between Two Points 2D?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>A</equation> in Area of a Rectangle is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Rectangle?"}
{"completion": " The Latex Code for equation Surface area of a Cuboidis <equation>S = 2lw + 2lh + 2wh</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Surface area of a Cuboid?"}
{"completion": " The equation for Spiral of Archimedes is: <equation>r = a \\\\theta</equation>. Here is the brief introduction of Spiral of Archimedes:\n        Latex code for Spiral of Archimedes.\n        \n: r\n: a\n: Angle Theta\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Spiral of Archimedes?"}
{"completion": " The Latex Code for equation Eccentricity of a Hyperbolais <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Eccentricity of a Hyperbola?"}
{"completion": " The equation for Surface area of a cube is: <equation>S = 6x^2</equation>. Here is the brief introduction of Surface area of a cube:\n        Latex code for Surface area of a cube.\n        \n: Surface\n: Length of a square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Surface area of a cube?"}
{"completion": " The equation for Eccentricity of an Ellipse is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of an Ellipse:\n        Latex code for Eccentricity of an Ellipse.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Eccentricity of an Ellipse?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbolic Paraboloid is: Length a.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>a</equation> in Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Spiral of Archimedesis <equation>r = a \\\\theta</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Spiral of Archimedes?"}
{"completion": " The Latex Code for equation Ellipsoidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Ellipsoid?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a Sphere is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>\\pi</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>A</equation> in Area of a Parallelogram is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Parallelogram?"}
{"completion": " The Latex Code for equation Elliptic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "How to write equation Elliptic Paraboloid?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>c</equation> in Elliptic Paraboloid is: Length of Axis z.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>c</equation> in Elliptic Paraboloid?"}
{"completion": " The Latex Code for equation Sphereis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Sphere?"}
{"completion": " The Latex Code for equation Area of a Triangleis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Triangle?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>\\pi</equation> in Surface area of a cylinder is: Constant of Pi.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>\\pi</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>l</equation> in Surface area of a Cuboid is: Length.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>l</equation> in Surface area of a Cuboid?"}
{"completion": " The related materials of Elliptic Paraboloid is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Elliptic Paraboloid?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>b</equation> in Elliptic Cone is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>b</equation> in Elliptic Cone?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipsoid is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>a</equation> in Ellipsoid?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>D</equation> in Plane is: Bias.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>D</equation> in Plane?"}
{"completion": " The related materials of Surface area of a Sphere is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Surface area of a Sphere?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Triangle is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Triangle?"}
{"completion": " The equation for Eccentricity of a Hyperbola is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola is: Eccentricity.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of a Hyperbola?"}
{"completion": " The equation for Area of a Circle is: <equation>A = \\\\pi r^2</equation>. Here is the brief introduction of Area of a Circle:\n        Latex code for Area of a Circle.\n        \n: Area\n: Constant ranging from 3.1415926-3.1415927\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Circle?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>B</equation> in Plane is: Coefficient of y.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>B</equation> in Plane?"}
{"completion": " The Latex Code for equation Area of a Ellipseis <equation>A = \\\\pi r_1 r_2</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Ellipse?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 2D is: Point 1.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x1,x2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Area of a Square is: <equation>A = x^2</equation>. Here is the brief introduction of Area of a Square:\n        Latex code for Area of a Square.\n        \n: Area\n: Length/Width of Square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Square?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbola is: Length b.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>b</equation> in Hyperbola?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>b</equation> in Elliptic Cone is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>b</equation> in Elliptic Cone?"}
{"completion": " The related materials of Elliptic Cone is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Elliptic Cone?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Cylindrical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>r</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Spherical Coordinates:\n        Latex code for Cartesian to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 2D is: Distance.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>d</equation> in Distance Between Two Points 2D?"}
{"completion": " The Latex Code for equation Elliptic Coneis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Elliptic Cone?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone is: Center Coordinates of Elliptic Cone.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Cone?"}
{"completion": " The Latex Code for equation Parabolais <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Parabola?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cylindrical to Spherical Coordinates:\n        Latex code for Cylindrical to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a cylinder is: Height.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>h</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Circle is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. Here is the brief introduction of Circle:\n        Latex code for Circle\n        \n: Coordinates of Circle Center\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Circle?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Cylindrical Coordinates:\n        Latex code for Cartesian to Cylindrical Coordinates.\n        \n: Cylindrical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Ellipsoid is: Center Coordinates of Ellipsoid.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x_0,y_0,z_0)</equation> in Ellipsoid?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 3D is: Point 1.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x1,x2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>w</equation> in Area of a Rectangle is: Width.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>w</equation> in Area of a Rectangle?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Circle is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Circle?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>C</equation> in Plane is: Coefficient of z.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>C</equation> in Plane?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Circle is: Coordinates of Circle Center.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x_0,y_0)</equation> in Circle?"}
{"completion": " The related materials of Sphere is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Sphere?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Square is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Square?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Area of a Circle is: Radius.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>r</equation> in Area of a Circle?"}
{"completion": " The Latex Code for equation Hyperbolic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "How to write equation Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Surface area of a cubeis <equation>S = 6x^2</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Surface area of a cube?"}
{"completion": " The Latex Code for equation Area of a Sectoris <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Sector?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>l</equation> in Surface area of a Cuboid is: Length.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>l</equation> in Surface area of a Cuboid?"}
{"completion": " The Latex Code for equation Distance Between Two Points 3Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Distance Between Two Points 3D?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbola is: Center Point.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x_0,y_0)</equation> in Hyperbola?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>h</equation> in Area of a Parallelogram is: Length of Height of parallelogram.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>h</equation> in Area of a Parallelogram?"}
{"completion": " The equation for Area of a Equilateral Triangle is: <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. Here is the brief introduction of Area of a Equilateral Triangle:\n        Latex code for Area of a Equilateral Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Equilateral Triangle?"}
{"completion": " The equation for Cartesian to Polar Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Polar Coordinates:\n        Latex code for Cartesian to Polar Coordinates.\n        \n: Polar Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Cartesian to Polar Coordinates?"}
{"completion": " The related materials of Area of a Circle is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Circle?"}
{"completion": " The equation for Area of a Circle is: <equation>A = \\\\pi r^2</equation>. Here is the brief introduction of Area of a Circle:\n        Latex code for Area of a Circle.\n        \n: Area\n: Constant ranging from 3.1415926-3.1415927\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Circle?"}
{"completion": " The equation for Surface area of a Cuboid is: <equation>S = 2lw + 2lh + 2wh</equation>. Here is the brief introduction of Surface area of a Cuboid:\n        Latex code for Surface area of a cuboid.\n        \n: Surface\n: Length\n: Width\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Surface area of a Cuboid?"}
{"completion": " The Latex Code for equation Surface area of a cylinderis <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Surface area of a cylinder?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y)</equation> in Cartesian to Polar Coordinates is: Polar Coordinates.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x,y)</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Circle is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Circle?"}
{"completion": " The equation for Hyperbola is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Hyperbola:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Hyperbola?"}
{"completion": " The related materials of Area of a Regular Polygon is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Regular Polygon?"}
{"completion": " The equation for Area of a Rhombus is <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Rhombus is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Rhombus?"}
{"completion": " The Latex Code for equation Hyperbolais <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Hyperbola?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbola is: Length a.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>a</equation> in Hyperbola?"}
{"completion": " The equation for Eccentricity of an Ellipse is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of an Ellipse is: Eccentricity.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>\\varepsilon</equation> in Eccentricity of an Ellipse?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Area of a Circle is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>r</equation> in Area of a Circle?"}
{"completion": " The Latex Code for equation Area of a Sectoris <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Area of a Sector?"}
{"completion": " The Latex Code for equation Area of a Ellipseis <equation>A = \\\\pi r_1 r_2</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Ellipse?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Cuboid is: Surface.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>S</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Area of a Equilateral Triangle is <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>. The meaning of symbol <equation>A</equation> in Area of a Equilateral Triangle is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Equilateral Triangle?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>C</equation> in Plane is: Coefficient of z.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>C</equation> in Plane?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Circle is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Circle?"}
{"completion": " The Latex Code for equation Cylindrical to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>l</equation> in Surface area of a Cuboid is: Length.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>l</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Spiral of Archimedes is: <equation>r = a \\\\theta</equation>. Here is the brief introduction of Spiral of Archimedes:\n        Latex code for Spiral of Archimedes.\n        \n: r\n: a\n: Angle Theta\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Spiral of Archimedes?"}
{"completion": " The equation for Area of a Trapezoid is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Trapezoid:\n        Latex code for Area of a Trapezoid.\n        \n: Area\n: Length of top of trapezoid\n: Length of bottom of trapezoid\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Trapezoid?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 2D is: Point 2.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Cuboid is: Surface.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>S</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>D</equation> in Plane is: Bias.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>D</equation> in Plane?"}
{"completion": " The related materials of Distance Between Two Points 3D is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Distance Between Two Points 3D?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid is: Center Coordinates of Elliptic Paraboloid..", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x_0,y_0,z_0)</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbolic Paraboloid is: Length b.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>b</equation> in Hyperbolic Paraboloid?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>x</equation> in Area of a Square is: Length/Width of Square.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>x</equation> in Area of a Square?"}
{"completion": " The equation for Hyperbolic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Hyperbolic Paraboloid:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Hyperbolic Paraboloid?"}
{"completion": " The related materials of Cartesian to Cylindrical Coordinates is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Cartesian to Cylindrical Coordinates?"}
{"completion": " The Latex Code for equation Ellipsoidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Ellipsoid?"}
{"completion": " The equation for Area of a Rectangle is: <equation>A = lw</equation>. Here is the brief introduction of Area of a Rectangle:\n        Latex code for Area of a Rectangle.\n        \n: Area\n: Width\n: Length\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Rectangle?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Paraboloid is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>a</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>w</equation> in Surface area of a Cuboid is: Width.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>w</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 3D is: Point 2.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(y1,y2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>R</equation> in Circle is: Radius.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>R</equation> in Circle?"}
{"completion": " The Latex Code for equation Surface area of a cylinderis <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Surface area of a cylinder?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a Cuboid is: Surface.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>S</equation> in Surface area of a Cuboid?"}
{"completion": " The equation for Eccentricity of a Hyperbola is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of a Hyperbola:\n        Latex code for Eccentricity of a Hyperbola.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Eccentricity of a Hyperbola?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>r</equation> in Spiral of Archimedes is: r.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>r</equation> in Spiral of Archimedes?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>a</equation> in Spiral of Archimedes is: a.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>a</equation> in Spiral of Archimedes?"}
{"completion": " The Latex Code for equation Area of a Equilateral Triangleis <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Equilateral Triangle?"}
{"completion": " The Latex Code for equation Eccentricity of a Hyperbolais <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Eccentricity of a Hyperbola?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Spherical Coordinates:\n        Latex code for Cartesian to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Cartesian to Spherical Coordinates?"}
{"completion": " The Latex Code for equation Area of a Rectangleis <equation>A = lw</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Rectangle?"}
{"completion": " The equation for Distance Between Two Points 2D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 2D:\n        Latex code for Distance Between Two Points 2D.\n        \n: Distance\n: Point 1\n: Point 2\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Distance Between Two Points 2D?"}
{"completion": " The Latex Code for equation Eccentricity of a Hyperbolais <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Eccentricity of a Hyperbola?"}
{"completion": " The equation for Eccentricity of an Ellipse is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of an Ellipse:\n        Latex code for Eccentricity of an Ellipse.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Eccentricity of an Ellipse?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(z1,z2)</equation> in Distance Between Two Points 3D is: Point 3.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(z1,z2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>A</equation> in Plane is: Coefficient of x.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Plane?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cylindrical to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>r</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_1</equation> in Area of a Trapezoid is: Length of top of trapezoid.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>x_1</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid is: Center Point.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x_0,y_0)</equation> in Hyperbolic Paraboloid?"}
{"completion": " The Latex Code for equation Elliptic Cylinderis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Elliptic Cylinder?"}
{"completion": " The equation for Eccentricity of an Ellipse is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of an Ellipse is: Eccentricity.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>\\varepsilon</equation> in Eccentricity of an Ellipse?"}
{"completion": " The related materials of Spiral of Archimedes is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Spiral of Archimedes?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>x</equation> in Area of a Square is: Length/Width of Square.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>x</equation> in Area of a Square?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_1</equation> in Area of a Trapezoid is: Length of top of trapezoid.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>x_1</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>\\theta</equation> in Spiral of Archimedes is: Angle Theta.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>\\theta</equation> in Spiral of Archimedes?"}
{"completion": " The Latex Code for equation Area of a Triangleis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Triangle?"}
{"completion": " The equation for Distance Between Two Points 2D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 2D:\n        Latex code for Distance Between Two Points 2D.\n        \n: Distance\n: Point 1\n: Point 2\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Distance Between Two Points 2D?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>r</equation> in Surface area of a cylinder is: Radius r.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>r</equation> in Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Elliptic Coneis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Elliptic Cone?"}
{"completion": " The related materials of Area of a Rhombus is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Area of a Rhombus?"}
{"completion": " The equation for Area of a Square is: <equation>A = x^2</equation>. Here is the brief introduction of Area of a Square:\n        Latex code for Area of a Square.\n        \n: Area\n: Length/Width of Square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Area of a Square?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 2D is: Point 2.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(y1,y2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Spiral of Archimedes is: <equation>r = a \\\\theta</equation>. Here is the brief introduction of Spiral of Archimedes:\n        Latex code for Spiral of Archimedes.\n        \n: r\n: a\n: Angle Theta\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Spiral of Archimedes?"}
{"completion": " The equation for Area of a Triangle is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Triangle:\n        Latex code for Area of a Triangle.\n        \n: Area\n: Length of Bottom of Triangle\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Area of a Triangle?"}
{"completion": " The equation for Eccentricity of an Ellipse is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of an Ellipse is: Eccentricity.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>\\varepsilon</equation> in Eccentricity of an Ellipse?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipsoid is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>a</equation> in Ellipsoid?"}
{"completion": " The Latex Code for equation Area of a Triangleis <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Triangle?"}
{"completion": " The equation for Area of a Rhombus is: <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. Here is the brief introduction of Area of a Rhombus:\n        Latex code for Area of a Rhombus.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Rhombus?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a cylinder is: Height.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>h</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Paraboloid is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>a</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Area of a Sector is <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Sector is: Area.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Area of a Sector?"}
{"completion": " The equation for Area of a Square is: <equation>A = x^2</equation>. Here is the brief introduction of Area of a Square:\n        Latex code for Area of a Square.\n        \n: Area\n: Length/Width of Square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Area of a Square?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>B</equation> in Plane is: Coefficient of y.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>B</equation> in Plane?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(y1,y2)</equation> in Distance Between Two Points 2D is: Point 2.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(y1,y2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipse is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>a</equation> in Ellipse?"}
{"completion": " The Latex Code for equation Cartesian to Cylindrical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Square is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Square?"}
{"completion": " The Latex Code for equation Sphereis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Sphere?"}
{"completion": " The equation for Area of a Sector is <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Sector is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Sector?"}
{"completion": " The equation for Eccentricity of an Ellipse is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of an Ellipse:\n        Latex code for Eccentricity of an Ellipse.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Eccentricity of an Ellipse?"}
{"completion": " The equation for Surface area of a cube is: <equation>S = 6x^2</equation>. Here is the brief introduction of Surface area of a cube:\n        Latex code for Surface area of a cube.\n        \n: Surface\n: Length of a square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Surface area of a cube?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>C</equation> in Plane is: Coefficient of z.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>C</equation> in Plane?"}
{"completion": " The Latex Code for equation Hyperbolic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Hyperbolic Paraboloid?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates is: Cylindrical Coordinates.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Eccentricity of a Hyperbola is: <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>. Here is the brief introduction of Eccentricity of a Hyperbola:\n        Latex code for Eccentricity of a Hyperbola.\n        \n: Eccentricity\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Eccentricity of a Hyperbola?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates is: Spherical Coordinates.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x,y,z)</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Sphere is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. The meaning of symbol <equation>R</equation> in Sphere is: Radius.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>R</equation> in Sphere?"}
{"completion": " The equation for Distance Between Two Points 3D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 3D:\n        Latex code for Distance Between Two Points 3D.\n        \n: Distance\n: Point 1\n: Point 2\n: Point 3\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Distance Between Two Points 3D?"}
{"completion": " The equation for Ellipsoid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipsoid:\n        Latex code for Ellipsoid.\n        \n: Center Coordinates of Ellipsoid\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Ellipsoid?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbola is: Length b.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>b</equation> in Hyperbola?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates is: Cylindrical Coordinates.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Parabola is: <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>. Here is the brief introduction of Parabola:\n        Latex code for Parabola.\n        \n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Parabola?"}
{"completion": " The Latex Code for equation Area of a Parallelogramis <equation>A = bh</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Parallelogram?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>a</equation> in Elliptic Cone is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>a</equation> in Elliptic Cone?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Trapezoid is: Height.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>h</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Plane is: <equation>Ax + By + Cz + D = 0</equation>. Here is the brief introduction of Plane:\n        Latex code for Parabola.\n        \n: Coefficient of x\n: Coefficient of y\n: Coefficient of z\n: Bias\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Plane?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>r</equation> in Surface area of a cylinder is: Radius r.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>r</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>b</equation> in Area of a Parallelogram is: Length of Base.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>b</equation> in Area of a Parallelogram?"}
{"completion": " The Latex Code for equation Spiral of Archimedesis <equation>r = a \\\\theta</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Spiral of Archimedes?"}
{"completion": " The equation for Surface area of a Cuboid is: <equation>S = 2lw + 2lh + 2wh</equation>. Here is the brief introduction of Surface area of a Cuboid:\n        Latex code for Surface area of a cuboid.\n        \n: Surface\n: Length\n: Width\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Surface area of a Cuboid?"}
{"completion": " The equation for Ellipse is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipse:\n        Latex code for Ellipse.\n        \n: Center Coordinates of Ellipse\n: Length of Axis a\n: Length of Axis b\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Ellipse?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>r</equation> in Spiral of Archimedes is: r.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Spiral of Archimedes?"}
{"completion": " The equation for Distance Between Two Points 2D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 2D:\n        Latex code for Distance Between Two Points 2D.\n        \n: Distance\n: Point 1\n: Point 2\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Distance Between Two Points 2D?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cylindrical to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>r</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>r</equation> in Surface area of a cylinder is: Radius r.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Elliptic Paraboloid is: Length of Axis y.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>b</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>A</equation> in Area of a Parallelogram is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Parallelogram?"}
{"completion": " The equation for Area of a Square is: <equation>A = x^2</equation>. Here is the brief introduction of Area of a Square:\n        Latex code for Area of a Square.\n        \n: Area\n: Length/Width of Square\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Square?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>r</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 3D is: Distance.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>d</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Area of a Circle is: <equation>A = \\\\pi r^2</equation>. Here is the brief introduction of Area of a Circle:\n        Latex code for Area of a Circle.\n        \n: Area\n: Constant ranging from 3.1415926-3.1415927\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Circle?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>h</equation> in Area of a Parallelogram is: Length of Height of parallelogram.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>h</equation> in Area of a Parallelogram?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>b</equation> in Elliptic Cone is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>b</equation> in Elliptic Cone?"}
{"completion": " The equation for Area of a Sector is <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Sector is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Sector?"}
{"completion": " The Latex Code for equation Parabolais <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Parabola?"}
{"completion": " The Latex Code for equation Sphereis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Sphere?"}
{"completion": " The Latex Code for equation Cartesian to Cylindrical Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Spiral of Archimedes is <equation>r = a \\\\theta</equation>. The meaning of symbol <equation>\\theta</equation> in Spiral of Archimedes is: Angle Theta.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>\\theta</equation> in Spiral of Archimedes?"}
{"completion": " The Latex Code for equation Hyperbolais <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>", "tag": "Math,Geometry", "prompt": "How to write equation Hyperbola?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>c</equation> in Ellipsoid is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>c</equation> in Ellipsoid?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>\\phi</equation> in Area of a Circle is: Constant ranging from 3.1415926-3.1415927.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>\\phi</equation> in Area of a Circle?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbolic Paraboloid is: Length b.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>b</equation> in Hyperbolic Paraboloid?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Area of a Circle is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>r</equation> in Area of a Circle?"}
{"completion": " The equation for Hyperbola is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. Here is the brief introduction of Hyperbola:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Hyperbola?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cylinder is: Surface.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>S</equation> in Surface area of a cylinder?"}
{"completion": " The equation for Elliptic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Elliptic Paraboloid:\n        Latex code for Elliptic Paraboloid.\n        \n: Center Coordinates of Elliptic Paraboloid.\n: Length of Axis x\n: Length of Axis y\n: Length of Axis z\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Elliptic Paraboloid?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>c</equation> in Elliptic Cone is: Length of Axis c.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>c</equation> in Elliptic Cone?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cube is: Surface.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>S</equation> in Surface area of a cube?"}
{"completion": " The Latex Code for equation Area of a Ellipseis <equation>A = \\\\pi r_1 r_2</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Ellipse?"}
{"completion": " The equation for Hyperbolic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Hyperbolic Paraboloid:\n        Latex code for Hyperbola.\n        \n: Length a\n: Length b\n: Center Point\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Hyperbolic Paraboloid?"}
{"completion": " The equation for Area of a Rectangle is: <equation>A = lw</equation>. Here is the brief introduction of Area of a Rectangle:\n        Latex code for Area of a Rectangle.\n        \n: Area\n: Width\n: Length\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Rectangle?"}
{"completion": " The Latex Code for equation Eccentricity of a Hyperbolais <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 + b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Eccentricity of a Hyperbola?"}
{"completion": " The equation for Surface area of a cylinder is: <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. Here is the brief introduction of Surface area of a cylinder:\n        Latex code for Surface area of a cylinder.\n        \n: Surface\n: Constant of Pi\n: Radius r\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Surface area of a cylinder?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>A</equation> in Area of a Square is: Area.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Area of a Square?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Triangle is: Height.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>h</equation> in Area of a Triangle?"}
{"completion": " The Latex Code for equation Sphereis <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>", "tag": "Math,Geometry", "prompt": "Show me the latex code of equation Sphere?"}
{"completion": " The equation for Cylindrical to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cylindrical to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>r</equation> in Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>b</equation> in Area of a Parallelogram is: Length of Base.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>b</equation> in Area of a Parallelogram?"}
{"completion": " The equation for Surface area of a cube is <equation>S = 6x^2</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cube is: Surface.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>S</equation> in Surface area of a cube?"}
{"completion": " The Latex Code for equation Cylindrical to Spherical Coordinatesis <equation>\\\\begin{array}{*{20}c} {r = R\\\\sin \\\\theta } & {R = \\\\sqrt {r^2 + z^2 } } & {} \\\\\\\\ {z = R\\\\sin \\\\theta } & {\\\\phi = \\\\theta } & {} \\\\\\\\ {\\\\theta = \\\\phi } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{r}{z}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Cylindrical to Spherical Coordinates?"}
{"completion": " The equation for Sphere is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 + \\\\left( {z - z_0 } \\\\right)^2 = R^2\\ </equation>. Here is the brief introduction of Sphere:\n        Latex code for Parabola.\n        \n: Center Coordinates of Sphere\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Sphere?"}
{"completion": " The equation for Area of a Circle is <equation>A = \\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Area of a Circle is: Radius.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>r</equation> in Area of a Circle?"}
{"completion": " The equation for Area of a Rectangle is: <equation>A = lw</equation>. Here is the brief introduction of Area of a Rectangle:\n        Latex code for Area of a Rectangle.\n        \n: Area\n: Width\n: Length\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Rectangle?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>A</equation> in Plane is: Coefficient of x.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>A</equation> in Plane?"}
{"completion": " The Latex Code for equation Area of a Rhombusis <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Area of a Rhombus?"}
{"completion": " The equation for Hyperbolic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbolic Paraboloid is: Length a.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>a</equation> in Hyperbolic Paraboloid?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>a</equation> in Elliptic Cone is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>a</equation> in Elliptic Cone?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is: <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. Here is the brief introduction of Cartesian to Spherical Coordinates:\n        Latex code for Cartesian to Spherical Coordinates.\n        \n: Spherical Coordinates\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Elliptic Paraboloid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. The meaning of symbol <equation>c</equation> in Elliptic Paraboloid is: Length of Axis z.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>c</equation> in Elliptic Paraboloid?"}
{"completion": " The equation for Ellipse is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Ellipse is: Length of Axis a.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>a</equation> in Ellipse?"}
{"completion": " The Latex Code for equation Area of a Circleis <equation>A = \\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Circle?"}
{"completion": " The Latex Code for equation Parabolais <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Parabola?"}
{"completion": " The equation for Area of a Parallelogram is <equation>A = bh</equation>. The meaning of symbol <equation>b</equation> in Area of a Parallelogram is: Length of Base.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>b</equation> in Area of a Parallelogram?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Elliptic Cylinder is: Length of Axis x.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>a</equation> in Elliptic Cylinder?"}
{"completion": " The equation for Elliptic Cone is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. The meaning of symbol <equation>b</equation> in Elliptic Cone is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>b</equation> in Elliptic Cone?"}
{"completion": " The related materials of Parabola is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Parabola?"}
{"completion": " The equation for Area of a Triangle is: <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. Here is the brief introduction of Area of a Triangle:\n        Latex code for Area of a Triangle.\n        \n: Area\n: Length of Bottom of Triangle\n: Height\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Triangle?"}
{"completion": " The Latex Code for equation Cartesian to Polar Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "What is the latex code of equation Cartesian to Polar Coordinates?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates is: Cylindrical Coordinates.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x,y,z)</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Trapezoid is: Height.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>h</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbola is: Length a.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>a</equation> in Hyperbola?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>h</equation> in Area of a Triangle is: Height.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>h</equation> in Area of a Triangle?"}
{"completion": " The Latex Code for equation Elliptic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Elliptic Paraboloid?"}
{"completion": " The equation for Ellipsoid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. Here is the brief introduction of Ellipsoid:\n        Latex code for Ellipsoid.\n        \n: Center Coordinates of Ellipsoid\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Ellipsoid?"}
{"completion": " The equation for Elliptic Cone is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }}</equation>. Here is the brief introduction of Elliptic Cone:\n        Latex code for Elliptic Cone.\n        \n: Center Coordinates of Elliptic Cone\n: Length of Axis a\n: Length of Axis b\n: Length of Axis c\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Elliptic Cone?"}
{"completion": " The equation for Surface area of a Cuboid is <equation>S = 2lw + 2lh + 2wh</equation>. The meaning of symbol <equation>h</equation> in Surface area of a Cuboid is: Height.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>h</equation> in Surface area of a Cuboid?"}
{"completion": " The Latex Code for equation Eccentricity of an Ellipseis <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Eccentricity of an Ellipse?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_1</equation> in Area of a Trapezoid is: Length of top of trapezoid.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>x_1</equation> in Area of a Trapezoid?"}
{"completion": " The equation for Area of a Rhombus is: <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. Here is the brief introduction of Area of a Rhombus:\n        Latex code for Area of a Rhombus.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Rhombus?"}
{"completion": " The related materials of Plane is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Plane?"}
{"completion": " The Latex Code for equation Area of a Equilateral Triangleis <equation>A = \\\\frac{{h^2 \\\\sqrt 3 }}{3}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Equilateral Triangle?"}
{"completion": " The equation for Eccentricity of an Ellipse is <equation>\\\\varepsilon = \\\\frac{{\\\\sqrt {a^2 - b^2 } }}{a}</equation>. The meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of an Ellipse is: Eccentricity.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>\\varepsilon</equation> in Eccentricity of an Ellipse?"}
{"completion": " The equation for Distance Between Two Points 2D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 2D is: Point 1.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x1,x2)</equation> in Distance Between Two Points 2D?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Hyperbola is: Center Point.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>(x_0,y_0)</equation> in Hyperbola?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>b</equation> in Area of a Triangle is: Length of Bottom of Triangle.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>b</equation> in Area of a Triangle?"}
{"completion": " The Latex Code for equation Area of a Rectangleis <equation>A = lw</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Area of a Rectangle?"}
{"completion": " The equation for Plane is <equation>Ax + By + Cz + D = 0</equation>. The meaning of symbol <equation>D</equation> in Plane is: Bias.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>D</equation> in Plane?"}
{"completion": " The equation for Circle is: <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. Here is the brief introduction of Circle:\n        Latex code for Circle\n        \n: Coordinates of Circle Center\n: Radius\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "What's the meaning of Circle?"}
{"completion": " The equation for Area of a Regular Polygon is <equation>A = \\\\frac{{nsr}}{2} = \\\\frac{{pr}}{2}</equation>. The meaning of symbol <equation>A</equation> in Area of a Regular Polygon is: Area.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>A</equation> in Area of a Regular Polygon?"}
{"completion": " The Latex Code for equation Cartesian to Polar Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Cartesian to Polar Coordinates?"}
{"completion": " The equation for Area of a Rectangle is <equation>A = lw</equation>. The meaning of symbol <equation>l</equation> in Area of a Rectangle is: Length.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>l</equation> in Area of a Rectangle?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>a</equation> in Hyperbola is: Length a.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>a</equation> in Hyperbola?"}
{"completion": " The equation for Elliptic Paraboloid is: <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>. Here is the brief introduction of Elliptic Paraboloid:\n        Latex code for Elliptic Paraboloid.\n        \n: Center Coordinates of Elliptic Paraboloid.\n: Length of Axis x\n: Length of Axis y\n: Length of Axis z\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Please give me detailed tutorial of Elliptic Paraboloid?"}
{"completion": " The Latex Code for equation Hyperbolic Paraboloidis <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = \\\\frac{{\\\\left( {z - z_0 } \\\\right)}}{c}\\ </equation>", "tag": "Math,Geometry", "prompt": "What is the equation of Hyperbolic Paraboloid?"}
{"completion": " The equation for Cartesian to Cylindrical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } & {} \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = z} & {z = z} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Cylindrical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Cartesian to Cylindrical Coordinates?"}
{"completion": " The equation for Cartesian to Spherical Coordinates is <equation>\\\\begin{array}{*{20}c} {x = R\\\\sin \\\\theta \\\\cos \\\\phi } & {R = \\\\sqrt {x^2 + y^2 + z^2 } } & {} \\\\\\\\ {y = R\\\\sin \\\\theta \\\\sin \\\\phi } & {\\\\phi = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} & {} \\\\\\\\ {z = R\\\\cos \\\\theta } & {\\\\theta = \\\\cos ^{ - 1} \\\\left( {\\\\frac{z}{{\\\\sqrt {x^2 + y^2 + z^2 } }}} \\\\right)} & {} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>r</equation> in Cartesian to Spherical Coordinates is: Radius.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>r</equation> in Cartesian to Spherical Coordinates?"}
{"completion": " The equation for Surface area of a cylinder is <equation>S = 2\\\\pi r^2 + 2\\\\pi rh</equation>. The meaning of symbol <equation>S</equation> in Surface area of a cylinder is: Surface.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>S</equation> in Surface area of a cylinder?"}
{"completion": " The Latex Code for equation Cartesian to Polar Coordinatesis <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Cartesian to Polar Coordinates?"}
{"completion": " The Latex Code for equation Distance Between Two Points 3Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Distance Between Two Points 3D?"}
{"completion": " The Latex Code for equation Distance Between Two Points 2Dis <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 }</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Distance Between Two Points 2D?"}
{"completion": " The Latex Code for equation Parabolais <equation>\\\\left( {y - y_0 } \\\\right)^2 = 4a\\\\left( {x - x_0 } \\\\right)</equation>", "tag": "Math,Geometry", "prompt": "How to write equation Parabola?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>b</equation> in Area of a Triangle is: Length of Bottom of Triangle.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>b</equation> in Area of a Triangle?"}
{"completion": " The equation for Area of a Sector is: <equation>A = \\\\frac{{\\\\theta r^2 }}{2}</equation>. Here is the brief introduction of Area of a Sector:\n        Latex code for Area of a Sector.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Sector?"}
{"completion": " The equation for Ellipsoid is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} + \\\\frac{{\\\\left( {z - z_0 } \\\\right)^2 }}{{c^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Ellipsoid is: Length of Axis b.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>b</equation> in Ellipsoid?"}
{"completion": " The equation for Elliptic Cylinder is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} + \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Elliptic Cylinder is: Center Coordinates of Elliptic Cylinder.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>(x_0,y_0)</equation> in Elliptic Cylinder?"}
{"completion": " The equation for Area of a Square is <equation>A = x^2</equation>. The meaning of symbol <equation>x</equation> in Area of a Square is: Length/Width of Square.", "tag": "Math,Geometry", "prompt": "Can you explain the symbol <equation>x</equation> in Area of a Square?"}
{"completion": " The equation for Distance Between Two Points 3D is: <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. Here is the brief introduction of Distance Between Two Points 3D:\n        Latex code for Distance Between Two Points 3D.\n        \n: Distance\n: Point 1\n: Point 2\n: Point 3\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you give me a brief introduction to Distance Between Two Points 3D?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Surface area of a Sphere is: Radius r.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Area of a Rhombus is: <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>. Here is the brief introduction of Area of a Rhombus:\n        Latex code for Area of a Rhombus.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "Can you explain Area of a Rhombus?"}
{"completion": " The equation for Cartesian to Polar Coordinates is <equation>\\\\begin{array}{*{20}c} {x = r\\\\cos \\\\theta } & {r = \\\\sqrt {x^2 + y^2 } } \\\\\\\\ {y = r\\\\sin \\\\theta } & {\\\\theta = \\\\tan ^{ - 1} \\\\left( {\\\\frac{y}{x}} \\\\right)} \\\\\\\\ \\\\end{array}</equation>. The meaning of symbol <equation>(x,y)</equation> in Cartesian to Polar Coordinates is: Polar Coordinates.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>(x,y)</equation> in Cartesian to Polar Coordinates?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 3D is: Point 1.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x1,x2)</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>b</equation> in Area of a Triangle is: Length of Bottom of Triangle.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>b</equation> in Area of a Triangle?"}
{"completion": " The Latex Code for equation Area of a Rectangleis <equation>A = lw</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Rectangle?"}
{"completion": " The equation for Area of a Ellipse is <equation>A = \\\\pi r_1 r_2</equation>. The meaning of symbol <equation>A</equation> in Area of a Ellipse is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>A</equation> in Area of a Ellipse?"}
{"completion": " The equation for Distance Between Two Points 3D is <equation>d = \\\\sqrt {\\\\left( {x_1 - x_2 } \\\\right)^2 + \\\\left( {y_1 - y_2 } \\\\right)^2 + \\\\left( {z_1 - z_2 } \\\\right)^2 }</equation>. The meaning of symbol <equation>d</equation> in Distance Between Two Points 3D is: Distance.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>d</equation> in Distance Between Two Points 3D?"}
{"completion": " The equation for Area of a Triangle is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>A</equation> in Area of a Triangle is: Area.", "tag": "Math,Geometry", "prompt": "What is the meaning of the symbol <equation>A</equation> in Area of a Triangle?"}
{"completion": " The equation for Surface area of a Sphere is <equation>S = 4\\\\pi r^2</equation>. The meaning of symbol <equation>r</equation> in Surface area of a Sphere is: Radius r.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>r</equation> in Surface area of a Sphere?"}
{"completion": " The equation for Circle is <equation>\\\\left( {x - x_0 } \\\\right)^2 + \\\\left( {y - y_0 } \\\\right)^2 = R^2</equation>. The meaning of symbol <equation>(x_0,y_0)</equation> in Circle is: Coordinates of Circle Center.", "tag": "Math,Geometry", "prompt": "Help me find the meaning of symbol <equation>(x_0,y_0)</equation> in Circle?"}
{"completion": " The Latex Code for equation Surface area of a Sphereis <equation>S = 4\\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Surface area of a Sphere?"}
{"completion": " The Latex Code for equation Area of a Rhombusis <equation>A = \\\\frac{{x_1 x_2 }}{2}</equation>", "tag": "Math,Geometry", "prompt": "Can you write equation Area of a Rhombus?"}
{"completion": " The equation for Area of a Ellipse is: <equation>A = \\\\pi r_1 r_2</equation>. Here is the brief introduction of Area of a Ellipse:\n        Latex code for Area of a Triangle.\n        \n: Area\n\n\nRelated Documents\n\n\nRelated Videos\n\n\n", "tag": "Math,Geometry", "prompt": "I am interested in Area of a Ellipse?"}
{"completion": " The Latex Code for equation Area of a Circleis <equation>A = \\\\pi r^2</equation>", "tag": "Math,Geometry", "prompt": "Please give me some hints on equation Area of a Circle?"}
{"completion": " The related materials of Hyperbolic Paraboloid is: ", "tag": "Math,Geometry", "prompt": "Can you help me find related materials of Hyperbolic Paraboloid?"}
{"completion": " The equation for Hyperbola is <equation>\\\\frac{{\\\\left( {x - x_0 } \\\\right)^2 }}{{a^2 }} - \\\\frac{{\\\\left( {y - y_0 } \\\\right)^2 }}{{b^2 }} = 1\\ </equation>. The meaning of symbol <equation>b</equation> in Hyperbola is: Length b.", "tag": "Math,Geometry", "prompt": "What is the meaning of <equation>b</equation> in Hyperbola?"}
{"completion": " The equation for Area of a Trapezoid is <equation>A = \\\\frac{1}{2}(x_1 + x_2 )h</equation>. The meaning of symbol <equation>x_2</equation> in Area of a Trapezoid is: Length of bottom of trapezoid.", "tag": "Math,Geometry", "prompt": "What does the symbol mean <equation>x_2</equation> in Area of a Trapezoid?"}