Dickson 1894 rule for generating Pythagorean triples
Use the sliders to change the values of m and n. If l=0 (m=1), changing k (n) will generate the Pythagorean family of triples. If k=1 (n=2) changing l (m) will generate Plato's family of triples.
Leonard E. Dickson,Lowest Integers Representing Sides of a Right Triangle,The American Mathematical Monthly, Vol. 1, No. 1 (Jan., 1894), pp. 6-11