The Triangle Altitudes Theorem in Hyperbolic Plane Geometry

TL;DR

This paper introduces a new formulation and proof of the triangle altitudes theorem in hyperbolic geometry, along with a discriminant to classify altitude configurations.

Contribution

It presents a novel formulation and proof of the theorem in hyperbolic geometry and introduces a discriminant for configuration classification.

Findings

New formulation of the triangle altitudes theorem in hyperbolic geometry

Proof of the theorem using hyperbolic geometric methods

Discriminant for distinguishing altitude configurations

Abstract

We provide a new formulation and proof of the triangle altitudes theorem in hyperbolic plane geometry, together with an easily computed discriminant to distinguish between different basic configurations of the altitudes of such a triangle.