I mean, it's correct that Pythagorean triples are not the same thing as the Pythagorean theorem, but "Pythagoras" (or at least the Pythagorean school) proved th

I mean, it's correct that Pythagorean triples are not the same thing as the Pythagorean theorem, but "Pythagoras" (or at least the Pythagorean school) proved things about modular arithmetic with the triples. The geometric interpretation was they were the measures of the sides of right triangles and that no other right triangles were "measurable" (that is, they could not be expressed as having 3 rational side lengths).