Pythagorean theorem
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
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.
Two right angles and the diagonal of a box
The theorem applied once gives the diagonal of a floor. Applied again, standing on the first result, it gives the diagonal of the room — and the pattern does not stop at three, which is where a fact about triangles quietly becomes the definition of distance.
The triangle that a globe gets wrong
On a sphere, a right triangle with legs of fifty and sixty degrees has a hypotenuse of seventy-two, not seventy-eight. The theorem is not approximately true there — it is false, and what replaces it says exactly how much room the surface has.
Named alongside it
The objects these essays reach for when they reach for this one.
Right angleCongruenceConstructionConverseCurvatureDe gua theoremDimensionDistanceGeodesicHyperbolic geometryHypercubeLaw of cosines