Hyperbolic and Circular Trigonometry and Application to Special Relativity

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.