Generator

pythagoras

A generator in the geometry library, called 15 times across 3 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.

pythagoras 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

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.

and half the rectangle — same base, apex on the parallel through the altitude ×1
four triangles and the tilted square fill the left square ×1
four triangles and the two upright squares fill the right square ×1
so the square and the rectangle are equal ×1
the altitude cuts the big square into exactly these two rectangles ×1
the angle at C is a right angle ×1
the eight triangles are all the same ×1
the long leg is b ×1
the short leg is a ×1
the square on the hypotenuse is c² ×1
the square on the leg has the leg's area squared ×1
the tilted square equals the two upright squares ×1
the tilted square is c² ×1
the triangle is half the square — same base, apex on the opposite side ×1
the two triangles are the same triangle turned ×1

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

pythagoras

At its defaults

What it checks while it draws

Where it is called

Euclid proves it without moving anything

Every triple, on one circle

Two squares, four triangles, and no algebra