Explorables

I teach mathematics to fourteen-year-olds who have already decided, most of them, that they are “not maths people.” I do not argue with them. I hand them a thing that moves.

Everything here runs in your browser, with no account and no scoreboard. Drag a point and a curve answers; add a term and a wave gets squarer; throw darts at a and π climbs out of the counting. Each figure has an essay beside it, because a thing that moves is a question, and a question deserves an honest answer rather than a badge.

The colours are stolen, cheerfully, from Oliver Byrne’s 1847 edition of Euclid, which replaced the letters of every proof with blocks of vermilion , ochre, and cobalt. He believed you could see a proof. So do I.

The figures

1. The Fourier drawer — stack sine waves until a square wave appears out of the roundness. Companion essay: Why it starts with a square wave.
2. π by darts — a Monte-Carlo estimate of π, one random point at a time, with the running guess plotted as it settles. Companion essay: What π actually measures.
3. The self-drawing pendulum — a damped pendulum swinging beside its own phase portrait. Companion essay: The pendulum that draws itself.
4. Bézier by hand — drag the control points, switch on the construction lines, and watch de Casteljau do the averaging. Companion essay: Bézier curves are just weighted averages.
5. The prime spiral — Ulam’s spiral, primes lit up, patterns that are half real and half wishful. Companion essay: Prime spirals and pattern-hunger.

And one essay with no toy attached: against gamification, which is the closest I come to a manifesto, kept dry on purpose.