Calculating $\pi$

import matplotlib.pyplot as plt
import numpy as np

xx, yy = 2 * np.random.rand(2, 10000) -1

inner = xx**2 + yy**2 < 1

4 * inner.sum() / xx.shape[0]

fig, ax = plt.subplots(1, figsize = (10, 10))
ax.scatter(xx, yy, alpha=.25, marker='.', c = ['r' if i else 'b' for i in inner])
ax.add_patch(plt.Circle((0, 0), 1, facecolor='none', edgecolor='r', linewidth=1, alpha=0.75))
ax.set_aspect('equal')

from numba import jit

@jit
def approx_pi():
    xx, yy = 2 * np.random.rand(2, 1000000) -1
    inner = xx**2 + yy**2 < 1
    pi = 4 * inner.sum() / xx.shape[0]
    return pi

approx = [approx_pi() for i in range(1000)]
sum(approx) / len(approx)