# Heron Angles, Heron Triangles, and Heron Parallelograms

## TL;DR

This paper introduces bijective parametrizations for Heron angles, Heron triangles, and Heron parallelograms, characterizing their rational side lengths, diagonals, and areas, thus advancing the understanding of these rational geometric figures.

## Contribution

It provides the first explicit bijective parametrizations linking Heron angles, Heron triangles, and Heron parallelograms, unifying their rational properties.

## Key findings

- Bijective parametrizations for Heron angles, triangles, and parallelograms.
- Complete characterization of rational sides, diagonals, and areas.
- Unified framework for Heron geometric figures.

## Abstract

Heron angle: both its sine and cosine are rational Heron triangle: all its sides and area are rational Heron Parallelogram: all its sides, diagonals and area are rational We give one-to-one (bijective) parametrizations for all three concepts.