Monte Carlo approximation of $\pi$

Solution P2.5.10

Note that this Monte Carlo method converges extremely slowly (to get each new decimal place we have to increase the number of random points by a factor of 10):

import math
import random

N = 10000

def f(x):
    return math.sqrt(1.-x**2)

pi = 0.
for i in range(N):
    xi, yi = random.random(), random.random()
    if yi <= f(xi):
        pi += 1.
pi *= 4 / N
print('pi is approximately {:.4f}'.format(pi))

The output is:

pi is approximately 3.1432