Matpic
mathematics, in pictures
Generator

unroll

A generator in the geometry library, called 6 times across 1 essays. Below: what it draws at its defaults and at each mode an essay asks for, what it checks while drawing, and everywhere it is used.

unroll is one function. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and if the generator changes, this page changes with it.

At its defaults

A disc unrolled into a triangleA disc cut into 12 concentric rings, and the same rings straightened and stacked. The longest is the outer circumference; the shortest is nearly a point; the stack is a triangle.area πr²base 2πr, height r — area ½ · 2πr · r

show: "disc"

A disc unrolled into a triangleA disc cut into 16 concentric rings, and the same rings straightened and stacked. The longest is the outer circumference; the shortest is nearly a point; the stack is a triangle.area πr²

show: "sequence"

More rings, straighter edgeThe same unrolling at three ring counts. The stack's sloping side is a staircase at every finite count and a straight line only in the limit.base 2πr, height r — area ½ · 2πr · r6 ringsbase 2πr, height r — area ½ · 2πr · r14 ringsbase 2πr, height r — area ½ · 2πr · r40 rings

What it checks while it draws

Collected by running the family and listening to lib/verify.js, not written here. The count is how many separate times this build put that claim to the test.

Where it is called

Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.

Geometry

A circle unrolled into a triangle

Take a disc apart into rings, straighten each one, and stack them. The result is a triangle whose base is the circumference and whose height is the radius — and its area is the disc's.

The whole library · What the figures prove