Pythagorean Triples and a New Pythagorean Theorem

TL;DR

This paper introduces a novel Pythagorean relation involving inscribed squares in right triangles, providing new methods to generate rational right triangles from existing ones.

Contribution

It presents a new Pythagorean theorem involving inscribed squares, offering a fresh approach to constructing rational right triangles.

Findings

Reciprocal relations satisfy a Pythagorean equality

New methods to generate rational right triangles

Insight into geometric properties of inscribed squares

Abstract

Given a right triangle and two inscribed squares, we show that the reciprocals of the hypotenuse and the sides of the squares satisfy an interesting Pythagorean equality. This gives new ways to obtain rational(integer)right triangles from a given one.