Monte Carlo Estimation of PI in Python

pi-monte-carlo.py

import random as r
import math as m

# Number of darts that land inside.
inside = 0
# Total number of darts to throw.
total = 1000

# Iterate for the number of darts.
for i in range(0, total):
  # Generate random x, y in [0, 1].
  x2 = r.random()**2
  y2 = r.random()**2
    # Increment if inside unit circle.
    if m.sqrt(x2 + y2) < 1.0:
      inside += 1

# inside / total = pi / 4
pi = (float(inside) / total) * 4

# It works!
print(pi)

Thank you! This helped me understand how to run it with x and y.

Here is a slightly faster version.

def square_pi(N):
    # square_pi(100000000) is fast and gives 4 digits. 
    xy = np.random.random((N, 2)) ** 2
    counts = np.sum((xy[:, 0] + xy[:, 1]) <= 1)

    print("pi was approximated at ::",4*counts/N)
    return 4*counts/N