monte_carlo_pi.py

#!/usr/bin/env python3

import sys
from random import random


def single_trial():
    """
    Generate a random 2 dimensional point between (0, 0) and (1, 1)
    and returns weather the distance to the origin is less than 1


     |^^-- ,         + (1, 1)
     |       \_  False
     |          \  
     |     True   \
     |             |
     |______________|
    (0, 0)
    """
    x, y = random(), random()
    return x**2 + y**2 < 1


def pi_approximation(n_trials):
    # run n trials
    count = sum(single_trial() for _ in range(n_trials))
    # count / n_trials ~= pi/4  =>  pi ~= 4*count/n_trials
    return 4.0 * count / n_trials


def main()
    if len(sys.argv) < 2:  # check if a command line argument is passed
        # if not, use the default
        n_trials = 1000000
        print("Using the default of {} trials".format(n_trials))
    else:
        # get the command line argument
        n_trials = int(sys.argv[1])
    print(pi_approximation(n_trials))

if __name__ == '__main__':
    main()