'''A function to use Monte Carlo methods to compute pi.'''

import random
import math

# This function randomly throws darts a board with a squared
# unit ircle and counts the number that end up inside the circle.
def montePi(numDarts):

    # Initially zero darts have hit inside the circle.
    inCircle = 0

    for i in range(numDarts):

        # randomly decide where the dart hits
        x = random.random()
        y = random.random()

        # calculate distance from the center of the circle
        d = math.sqrt(x**2 + y**2)

        # if inside the circle, increment our counter
        if d <= 1:
            inCircle = inCircle + 1

    # pi is the percentage that fell inside the unit circle,
    # times four because we are only looking at 1/4 of the circle.
    pi = inCircle/numDarts * 4

    return pi