Matpic
mathematics, in pictures
Generator

conic

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.

conic 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 cone cut to give an ellipseA double cone intersected by a plane tilted 24 degrees from horizontal.

show: "all"

Four conic sections from one coneCircle, ellipse, parabola and hyperbola, produced by tilting a single cutting plane further and further.circleplane levelellipsetilted a littleparabolaparallel to the sidehyperbolasteeper still

show: "dandelin"

Dandelin's spheresTwo spheres inscribed in the cone, one above the cutting plane and one below, each touching the plane at a single point. Those two points are the foci of the elliptical section.each sphere touches the conearound a dashed circle……and touches the planeat one point each:the two foci

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

One cone, four curves

The circle, the ellipse, the parabola and the hyperbola look like four separate objects with four separate equations. They are one object, cut at four angles.

The whole library · What the figures prove