Tagged “calculus”

2 essays.

1. 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.

2. 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.