A simple method for generating rational triangles

TL;DR

This paper introduces a straightforward method for generating rational triangles by utilizing Pythagorean rationals, which are ratios of integer leg lengths in Pythagorean triangles, leading to two families of rational-sided triangles.

Contribution

The paper presents a novel approach to generate rational triangles using Pythagorean rationals, expanding the understanding of rational geometric figures.

Findings

Derived new geometrical formulas for rational triangles

Defined Pythagorean rationals as ratios of integer legs

Generated two families of rational triangles

Abstract

In the early part of the paper, various geometrical formulas are derived. Then, at some point in the paper, the concept of a Pythagorean rational is introduced. A Pythagorean rational is a rational number which is the ratio of two integers which are the leglengths of a Pythagorean triangle. Using the idea of Pythagorean rationals, we generate two families of rational triangles. We define a rational triangle to be a triangle with rational sidelengths and area.