An Introduction to Hyperbolic Barycentric Coordinates and their Applications

TL;DR

This paper introduces hyperbolic barycentric coordinates, called gyrobarycentric coordinates, explaining their development from Einstein's velocity addition law and exploring their applications in hyperbolic geometry.

Contribution

It presents a comprehensive overview of hyperbolic barycentric coordinates and their derivation from relativistic velocity addition, highlighting their practical applications.

Findings

Hyperbolic barycentric coordinates extend Euclidean barycentric concepts to hyperbolic geometry.

The paper demonstrates applications in relativistic velocity models.

Provides a mathematical framework connecting Einstein's law to hyperbolic coordinate systems.

Abstract

Barycentric coordinates are commonly used in Euclidean geometry. The adaptation of barycentric coordinates for use in hyperbolic geometry gives rise to hyperbolic barycentric coordinates, known as gyrobarycentric coordinates. The aim of this article is to present the road from Einstein's velocity addition law of relativistically admissible velocities to hyperbolic barycentric coordinates along with applications.