GENERATING PYTHAGOREAN TRIPLES OF A GIVEN HEIGHT

The height of a Pythagorean triple (a, b, c) is defined as the difference c- b. In this paper, building on the Height-Excess Enumeration Theorem, we show how to generate primitive Pythagorean triples of a given height using powers of a single matrix. Then, we briefly discuss other matrices that both map any Pythagorean triple to another and also preserve a triple's height. We also note how Pythagorean triples with a given leg difference can be generated using matrices.