Estimates pi using a Monte-Carlo method

numpi.py

import numpy as np
import numpy.random as random

iters = 10e6

# 1. The equation of the area of a unit circle is `ac = pi * 1^2 = pi'
# 2. The area of a 2x2 square is `as = 2^2 = 4'
# 3. The probability of a random point being in the circle is pi / 4
# 4. Given a random point, the point is in the circle if the point's
#    radius from the centre is less or equal to 1
# 5. If the proportion of points inside the circle is multiplied by 4,
#    this value will be an approximation of pi

# Random values between -1 and 1
x = 2 * random.random(iters) - 1
y = 2 * random.random(iters) - 1
r = np.sqrt(x**2 + y**2)

# Number of points inside the circle
inside = (r <= 1).sum()

pi = 4 * (inside / iters)
print("Pi=", pi)