#!/urs/bin/env python3

"""
pi_recursive.py
Program to recursively calculate pi.
@author Richard White
@version 2018-03-14
"""

import math

def recurse(n):
    """recursively performs a summation that can be used
    to calculate pi. Maximum recursive depth is 997.
    """
    if n == 1:
        return 1
    else:
        return 1/(n * n) + recurse(n - 1)

def main():
    n = int(input("Enter recursion depth: "))

    my_pi = math.sqrt(6 * recurse(n))
    print("My pi: " + str(my_pi))
    print("math.pi: " + str(math.pi))
    percent_difference = abs(my_pi - math.pi) / math.pi * 100
    print("Percent difference: " + str(percent_difference))
    print("The number of iterations to get within 0.1% is 304 (by trial and error)")

    print("Solving with iteration!")
    sum = 0
    for i in range(n, 0, -1):
        sum += 1/(i * i)
    my_new_pi = math.sqrt(6 * sum)
    print(my_new_pi)
    percent_difference = abs(my_new_pi - math.pi) / math.pi * 100
    print("Percent difference: " + str(percent_difference))

if __name__ == "__main__":
    main()