Three integers satisfying a² + b² = c² form a Pythagorean triple, which can be drawn as a right triangle, or a point (a/c, b/c) on the unit circle. Amazing fact: starting with the four Pythagorean triples (±1,0,1), (0,±1,1) all others can be generated via hyperbolic reflections.pic.twitter.com/XORBHcbM1Z
Restricted to the unit circle, hyperbolic transformations are equivalent to projective transformations, and can be expressed as 3x3 matrices. Thus all Pythagorean triples (viewed as vectors) can be generated by applying 3x3 matrices. This leads to https://en.wikipedia.org/wiki/Tree_of_primitive_Pythagorean_triples ….