"""This module contains a code example related to
Think Python, 2nd Edition
by Allen Downey
http://thinkpython2.com
Copyright 2015 Allen Downey
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)
term = factor * num / den
total += term
if abs(term) < 1e-15:
break
k += 1
return 1 / total
print(estimate_pi())