A Taxonomy Based on Integer-Sided Parametrizations and Area-Perimeter Invariants

Abstract

This study explores Heron triangles, which are unique triangles characterized by integer side lengths and areas. It classifies various types, including Pythagorean, consecutive, isosceles, and integral Heron triangles, and examines their mathematical properties such as semiperimeters, inradii, circumscribed radii, and heights. By presenting definitions, illustrations, and detailed proofs of theorems, this paper aims to deepen understanding and provide a foundation for further mathematical applications.