PROTOTYPE — second Weights & Measures sketch, reusing the Ruler Simulator's chassis. Polar-coordinate math (angle ↔ click position) unit-tested before wiring in. No hil-shell/session-logger yet.

PROTRACTOR SIMULATOR

Read and place angles — and see exactly where π comes from
Reading it: line up the baseline (the flat edge) with one side of the angle, with the vertex sitting exactly on the center dot. Read where the other side crosses the curved edge — that's the angle in degrees.

Where π actually comes from

This whole curved edge — one full sweep from 0° to 180° — is exactly half of a circle. And a circle's relationship between its curve and a straight measurement is precisely what π is (the same idea covered in Calculator Explorer's π key deep-dive). Angles are usually measured two ways:

radians = degrees × (π / 180)
A full circle (360°) = 2π radians  ·  this protractor's whole range (180°) = π radians

So 90° — a plain right angle — is exactly π/2 radians, about 1.5708. Every angle you read on this protractor has a radian value hiding right behind the degree number.

Practice mode shows both values together every time, so the connection stays visible instead of feeling like two unrelated units.