Monte Carlo (calculate π using random numbers)

carlo.py

#!/usr/bin/env python

from random import random
from math import pow
from math import sqrt

def pi(sample):
    
    total = 0.0
    found = 0.0
    
    for i in range(sample):
        
        x = random()
        y = random()
        
        if sqrt(x * x + y * y) <= 1:
            found += 1
        
        total += 1
    
    return found / total * 4

# 3.14159...
print pi(10000000)


def integral(sample):
    
    total = 0.0
    found = 0.0
    
    for i in range(sample):
        
        x = random()
        y = random()
        
        if y <= pow(x, 2):
            found += 1
        
        total += 1
    
    return found / total

# 0.3333333...
print integral(10000)