2.22_repeated_sqrt.py

from math import sqrt
for n in range(1, 60):
    r = 2.0
    for i in range(n):
        r = sqrt(r)
    for i in range(n):
        r = r**2
    print '%d times sqrt and **2: %.16f' % (n, r)

"""
26 times sqrt and **2: 1.9999999917775542
27 times sqrt and **2: 1.9999999917775542
28 times sqrt and **2: 1.9999999917775542
29 times sqrt and **2: 1.9999999917775542
30 times sqrt and **2: 1.9999999917775542
31 times sqrt and **2: 1.9999999917775542
32 times sqrt and **2: 1.9999990380770896
33 times sqrt and **2: 1.9999971307544144
34 times sqrt and **2: 1.9999971307544144
35 times sqrt and **2: 1.9999971307544144
36 times sqrt and **2: 1.9999971307544144
37 times sqrt and **2: 1.9999971307544144
38 times sqrt and **2: 1.9999360966436217
39 times sqrt and **2: 1.9999360966436217
40 times sqrt and **2: 1.9999360966436217
#After 40 iteration the results vary from demo...?
41 times sqrt and **2: 1.9994478907329654
42 times sqrt and **2: 1.9984718365144798
43 times sqrt and **2: 1.9965211562778555
44 times sqrt and **2: 1.9965211562778555
45 times sqrt and **2: 1.9887374575497223
46 times sqrt and **2: 1.9887374575497223
47 times sqrt and **2: 1.9887374575497223
48 times sqrt and **2: 1.9887374575497223
49 times sqrt and **2: 1.8682459487159784
50 times sqrt and **2: 1.6487212645509468
51 times sqrt and **2: 1.6487212645509468
52 times sqrt and **2: 1.0000000000000000
53 times sqrt and **2: 1.0000000000000000
54 times sqrt and **2: 1.0000000000000000
55 times sqrt and **2: 1.0000000000000000
56 times sqrt and **2: 1.0000000000000000
57 times sqrt and **2: 1.0000000000000000
58 times sqrt and **2: 1.0000000000000000
59 times sqrt and **2: 1.0000000000000000
"""