Tagged “teaching”

5 essays.

1. Against gamification

   May 24, 2026 · 4 min

   The case against points, badges, streaks, and leaderboards in the maths classroom — made plainly, without slogans. On the overjustification effect, Goodhart's law, and rewarding the thing itself.

2. Prime spirals and pattern-hunger

   May 3, 2026 · 4 min

   Ulam's spiral lights up the primes and, unnervingly, they fall along diagonal lines. Some of those lines are real mathematics and some are the mind inventing order. A companion to the prime-spiral toy, on the honest uses of a suggestive picture.

3. Bézier curves are just weighted averages

   April 12, 2026 · 3 min

   The smooth curve behind every font and vector drawing is nothing more grand than averaging, done over and over. A companion to the Bézier toy, on de Casteljau's construction and why the curve stays inside its own cage.

4. The pendulum that draws itself

   March 22, 2026 · 4 min

   A swinging pendulum has two numbers at every instant — where it is and how fast it's moving. Plot one against the other and the motion draws a spiral. A companion to the pendulum toy, on phase space and where the energy goes.

5. Why the Fourier drawer starts with a square wave

   February 9, 2026 · 4 min

   A square wave is the rudest thing you can ask a sum of smooth curves to build — which is exactly why it belongs first. On odd harmonics, rotating vectors, and the little overshoot that never goes away.