Concept
Law of cosines
The relation giving the third side of any triangle from the other two and the angle between them, whose extra term vanishes at a right angle.
Named by 2 essays across one field — 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.
The rope that squares a corner
The theorem turns two sides into a third. Run it backwards and it turns three lengths into a right angle — which is a different statement, needs its own proof, and is the only one of the two that has ever been used to build anything.
Named alongside it
The objects these essays reach for when they reach for this one.
AreaCongruenceConstructionConverseCosineDissectionHypotenuseIncommensurabilityPythagorean theoremPythagorean triplesRight angleRight triangle