Pythagorean triples
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
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.
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.
BijectionCongruenceConicConstructionConverseDescentHypotenuseLaw of cosinesParametrisationPrimitive tripleProjectionPythagorean theorem