pi-from-random.py

import random

def solve():
    '''
    area of unit circle at (0.5, 0.5) = pi * (0.5 ^ 2)
    area of unit trangle at (0.5, 0.5) = 1 * 1
    the ratio of the number of points that fall in the circle to the number 
    of all points will approximate the ratio of the area of the circle to 
    the area of the entire square.
    '''
    N = 1000000
    i = 0
    for _ in range(N):
        x, y = random.random(), random.random()
        if (x - 0.5) ** 2 + (y - 0.5) ** 2 <= 0.25: i += 1
    return 4 * i / N

print(solve())