archimedes.py

import math


def side_length(n):
    """
    return the side length of a polygon inscribed in a unit circle

    The number of sides that the polygon has is (2 ** n) * 6
    """
    if n == 0:
        return 1.0
    l0 = (side_length(n - 1) / 2)
    l1 = 1 - math.sqrt(1 - l0**2)
    return math.sqrt(l0**2 + l1**2)


def pi(n):
    return (2**n * 3) * side_length(n)


def main():
    print pi(500)


if __name__ == "__main__":
    main()