Sandbox::https://github.com/AllenDowney/ThinkPython2/blob/master/code/pi.py

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"""This module contains a code example related to

Think Python, 2nd Edition

by Allen Downey

https://greenteapress.com/wp/think-python-2e/

License: http://creativecommons.org/licenses/by/4.0/

"""

from __future__ import print_function, division

import math

def factorial(n):

"""Computes factorial of n recursively."""

if n == 0:

return 1

else:

recurse = factorial(n-1)

result = n * recurse

return result

def estimate_pi():

"""Computes an estimate of pi.

Algorithm due to Srinivasa Ramanujan, from

http://en.wikipedia.org/wiki/Pi

"""

total = 0

k = 0

factor = 2 * math.sqrt(2) / 9801

while True:

num = factorial(4*k) * (1103 + 26390*k)

den = factorial(k)**4 * 396**(4*k)

total += num / den

term = factor * num/den

if abs(term) < 1e-15:

break

k += 1

return 1 / (factor * total)

print(estimate_pi())