buffon_needle.py

'''
Buffon's Needle Experiment

Inspired by Werner Krauth, http://www.lps.ens.fr/~krauth/index.php/Main_Page
'''

import random
import math

def buffon_needle(throws, needle_length, cracks_distance):
    print('Buffon\'s Needle Experiment')
    print('needle = ' + str(needle_length) + ', crack = ' + str(cracks_distance))
    print('\n')
    print('Hits          Estimate of PI')

    if needle_length > cracks_distance:
        raise Exception('The distance of cracks must be greater or equal than the length of the needle.')

    hits = 0
    for i in range(throws):
        x_center = random.uniform(0, cracks_distance / 2)  # random center x

        tau = 2  # τ, orientation
        while tau > 1:
            dx = random.uniform(0, 1)
            dy = random.uniform(0, 1)
            tau = math.sqrt(dx ** 2 + dy ** 2)

            if tau <= 1:
                xtip = x_center - (needle_length / 2) * dx / tau
                if xtip < 0:  # intersect
                    hits += 1

    # pi = 2*l*n / t*h
    c = 2 * needle_length * throws
    d = cracks_distance * hits
    print(str(hits) + '          ' + str(c / d))

hits = buffon_needle(throws=5000, needle_length=1, cracks_distance=2)