one way to see 3 methods.
If I may refer to Heilbron's 'geometry civilized' p151,
as one of the cleanest summaries of pythagorean triplets I've run across.
Set: Generation Triplet
Pythagorean n, any odd number n,n^21)/2,(n^2+1)/2
Platonic n, any even number n,(n^2)/41.(n^2)4+1
Euclidean x,y any unequal numbers x^2y^2,2xy,x^2+y^2
I personally found the odd case is , with some work, obvious as simply building squares on a plane. Rather enlightening an approach and exercise.
