Monte Carlo Method for Calculating Pi

MonteCarloPi.py

import math
import random

def coin_flip(flip_count):

	total_in_circle = 0.0
		
	for i in range(0, int(flip_count)):

		x_coord = random.uniform(-1.0, 1.0)
		y_coord = random.uniform(-1.0, 1.0)

		if x_coord*x_coord + y_coord*y_coord <= 1:
			total_in_circle += 1

	experimental_pi = 4.0*total_in_circle/flip_count
	return experimental_pi

def trial_average():

	flip_count = 100.0
	cumulative_pi = 0.0
	TRIAL_COUNT = 1000

	for j in range(0, 3):
		for i in range(0, 1001):
			
			# running total of pi
			cumulative_pi += coin_flip(flip_count)
			
			# prints only after the final trial
			if i % 1000 == 0 and i > 0:
				pi = cumulative_pi/(TRIAL_COUNT)
				total_in_circle = pi*flip_count/4
				proportion = total_in_circle/flip_count
				p = pi/4
				q = 1 - pi/4

				print "Flip count: "+ str(flip_count)
				print "Proportion inside unit cirle: " + str(proportion)
				print "Computed pi: " + str(pi)
				print "Expected number of successful trials (mu): " + str(pi*flip_count/4)
				print "Expected stddev of successful trials (sigma): " + str(math.sqrt(flip_count*p*q)) + "\n"

		# resets pi's total and increases amount of flips
		cumulative_pi = 0.0
		flip_count = flip_count*10

trial_average()