Hyperbolic and Circular Trigonometry and Application to Special Relativity

TL;DR

This paper explores hyperbolic and circular trigonometry, providing a geometric interpretation of special relativity that enhances understanding of Lorentz transformations and relativistic kinematics.

Contribution

It introduces a geometric framework based on hyperbolic and circular trigonometry to interpret special relativity, offering new conceptual tools for education.

Findings

Hyperbolic trigonometry offers a simple interpretation of Lorentz transformations.

Geometric approach clarifies relativistic kinematics.

Alternative trigonometric frameworks can enhance teaching methods.

Abstract

We discuss the most elementary properties of the hyperbolic trigonometry and show how they can be exploited to get a simple, albeit interesting, geometrical interpretation of the special relativity. It yields indeed a straightforword understanding of the Lorentz transformation and of the relativistic kinematics as well. The geometrical framework adopted in the article is useful to disclose a wealth of alternative trigonometries not taught in undergraduate and graduate courses. Their introduction could provide an interesting and useful conceptual tool for students and teachers.