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README.md

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-# pi-calculation-with-catalan-numbers
-This repository contains a Python script that calculates the digits of π (pi) using a novel algorithm based on Catalan numbers and fixed-point arithmetic. The algorithm efficiently computes the digits of π by leveraging the properties of Catalan numbers, making it a unique and effective method for high-precision calculations.
+# π Calculation with Catalan Numbers
+
+This repository contains a Python script to calculate the digits of π using Catalan numbers and fixed-point arithmetic.
+
+## Introduction
+
+Calculating the digits of π has been a topic of interest for mathematicians and computer scientists alike. This project introduces a novel algorithm for π calculation that leverages Catalan numbers and fixed-point arithmetic.
+
+## Algorithm
+
+The series representation used in this algorithm is:
+
+\[ \pi = 3 + 6 \sum_{n=1}^{\infty} \frac{(2n - 1) \cdot C_n}{(2n + 1) \cdot 16^n} \]
+
+Where \( C_n \) is the nth Catalan number.
+
+## Implementation
+
+The implementation of the algorithm in Python can be found in the `pi_gmpy.py` file.
+
+## Usage
+
+To use the script, run the following command in your terminal:
+
+```sh
+python pi_gmpy.py
+```
+
+You will be prompted to enter the number of digits of π you want to calculate.
+
+## Example
+
+```sh
+$ python pi_gmpy.py
+How many digits of π? : 100
+π = 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679...∞
+```
+
+## License
+
+This project is licensed under the MIT License - see the LICENSE file for details.