DDC-41: Monte-Carlo approximation of pi

A data challenge a day helps you master machine learning

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Each post is an exercise that helps you learn about data in Python.

Try to solve the exercise before checking my solution at the bottom of the post 🤓

You can share your solution or visualization in the comments!

Today’s challenge

The irrational number π can be empirically approximated by randomly sampling points in a square with boundaries [-1,1,-1,1], counting the number of random points that are also in the unit circle (defined as (x^2+y^2)<1), and multiplying their ratio by 4.

Implement this approximation as shown below. Each plotted location is a random (x,y) pair drawn from a uniform distribution between -1 and +1, and the coordinate is a green “x” if it’s outside the circle, and a yellow dot if it’s inside the circle. In the figure title, c is the number of points inside the circle. As you increase N, the approximation gets closer to π.

Yes, it looks a bit like the flag of Brazil.

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Scroll down for the solution…

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A steaming pie in the shape of a pi symbol being cut by a pirate with a hat with a pi symbol

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keep scrolling!

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import numpy as np
import matplotlib.pyplot as plt

n = 10_000
x = np.random.uniform(-1,1,n)
y = np.random.uniform(-1,1,n)
D = x**2+y**2

plt.plot(x[D>1],y[D>1],'gx',markersize=3)
plt.plot(x[D<1],y[D<1],'y.',markersize=2)
plt.gca().set(title=f'4c/N = {4*(D<1).sum()/n:.5f}\nN = {n}',
              aspect='equal', frame_on=False,
              xticks=[],yticks=[])
plt.show()