Notebooks as Posts: A Python Demo

This post is written as a Quarto .qmd document rather than plain Markdown. The prose you’re reading and the code below live in the same source file, and the code actually runs: Quarto executes it at build time via Jupyter, then hands the rendered Markdown — prose, code, and figures — to Hugo, which lays it out with the site’s usual typography, table of contents, and tags.

Here’s a small numerical experiment: approximating $\pi$ by sampling random points in a unit square and checking what fraction land inside the inscribed circle.

import numpy as np

rng = np.random.default_rng(seed=42)
n = 20_000
x, y = rng.uniform(-1, 1, n), rng.uniform(-1, 1, n)
inside = x**2 + y**2 <= 1
estimate = 4 * inside.sum() / n
estimate

np.float64(3.1384)

That estimate should be somewhere close to the real thing:

A plot makes the sampling easier to see than the number alone does — points inside the circle in one color, points outside in another:

import matplotlib.pyplot as plt

fig, ax = plt.subplots(figsize=(5, 5))
ax.scatter(x[inside], y[inside], s=2, color="#a8071a")
ax.scatter(x[~inside], y[~inside], s=2, color="#888")
ax.set_aspect("equal")
ax.set_xticks([])
ax.set_yticks([])
for spine in ax.spines.values():
    spine.set_visible(False)
plt.show()

The point of this post isn’t the Monte Carlo estimate itself — it’s that this whole thing (code, output, and figure) regenerates automatically whenever the source .qmd changes, the same way the statistics page regenerates from live GitHub data rather than being hand-updated.