Hyperbolic trigonometry in two-dimensional space-time geometry

By, analogy with complex numbers, a system of hyperbolic numbers call be introduced in the same way: {z = x + hy; h(2) = 1 x, y is an element of R}. As complex numbers are linked to the Euclidean geometry, so this system of numbers is linked to the pseudo-Euclidean plane geometry (space-time geometry). In this paper we will show how this system of numbers allows, by means of a Cartesian representation, an operative definition of hyperbolic functions rising the invariance with respect to special relativity Lorentz group. From this definition, by using elementary mathematics and an Euclidean approach, it is straightforward to formalise the pseudo-Euclidean trigonometry in the Cartesian plane with the same coherence as the Euclidean trigonometry.