num-pi.py

import matplotlib.pyplot as plt
import numpy as np

# set seed for reproduceable
np.random.seed(123)

ind = np.arange(1, 40_001)
x = np.random.random(40_000)
y = np.random.random(40_000)
radius = (x**2 + y**2)**.5 
in_circle = radius < 1
cumulative = 4*np.cumsum(in_circle)/ind

fig, ax = plt.subplots(ncols=2, figsize=(8,4))
ax[0].scatter(x, y, alpha=.01, c=in_circle)
ax[1].plot(cumulative)
ax[1].set_ylim(3.12, 3.18)