Concept
Hypotenuse
2 essays name this object, across one field. What follows is each of them, and the objects they name alongside it.
Also named here as right triangle — the same set of essays touches all of them, so they are one junction rather than several.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
AreaDissectionRight triangleAltitudeCongruenceCosineIncommensurabilityLaw of cosinesParallel linesShearSimilar triangles