There is a known correspondence between rational points on the unit circle and Pythagorean triples. Using problem-posing strategies, such as those found in Brown and Walter’s book The Art of Problem Posing, we will explore high-dimensional analogues of Pythagorean Triples such as by giving classifications or generalizing the generating formula. Beginning with a visual aid, in the form of a lattice, our generalization will proceed via the stereographic projection of rational points $S^n$ sphere.

K. Conrad, https://kconrad.math.uconn.edu/blurbs/ugradnumthy/pythagtriple.pdf.