Right triangle
Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.
Two squares, four triangles, and no algebra
The Pythagorean theorem is usually met as a formula to be memorised. It is much better met as a rearrangement that can be checked by eye.
Euclid proves it without moving anything
The rearrangement proof cuts and slides. Euclid's does neither — it shows that a square and a rectangle are each exactly twice the same triangle, seen from opposite sides, and that is harder to hold in the head for a reason worth understanding.
Every triple, on one circle
Draw a line of rational slope through a single point of a circle. Wherever it comes out is a rational point, and clearing the denominators turns it into a Pythagorean triple — so every triple there is comes from one line through one point.
Named alongside it
The objects these essays reach for when they reach for this one.
HypotenuseAreaDissectionAltitudeBijectionCongruenceConicCosineDescentIncommensurabilityLaw of cosinesParallel lines