Quadratic sequences in Pythagorean triples

Abstract

Using the Euclid's formula, we obtain an alternative formula for generating Pythagorean triples, both primitive and non-primitive. It easy to classify Pythagorean triples using this formula based on the divisibility of the leg of a Pythagorean triple by any positive integer. The differences in lengths between the hypotenuse and the legs of a Pythagorean triple obtained by this alternative formula form Quadratic sequences. These quadratic sequences have applications in various fields such as tiling.