Hyperbolic trigonometry in two-dimensional space-time geometry
Catoni, Francesco ; Cannata, Roberto ; Catoni, Vincenzo ; Zampetti, Paolo
arXiv, 0508011 / Harvested from arXiv
Text on arXiv
By analogy with complex numbers, a system of hyperbolic numbers can be introduced in the same way: z=x+h*y with h*h=1 and x,y real numbers. 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 using the invariance respect to special relativity Lorentz group. From this definition, by using elementary mathematics and an Euclidean approach, it is straightforward to formalize the pseudo-Euclidean trigonometry in the Cartesian plane with the same coherence as the Euclidean trigonometry.
Publié le : 2005-08-03
Classification:  Mathematical Physics 
@article{0508011,
     author = {Catoni, Francesco and Cannata, Roberto and Catoni, Vincenzo and Zampetti, Paolo},
     title = {Hyperbolic trigonometry in two-dimensional space-time geometry},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0508011}
}

Catoni, Francesco; Cannata, Roberto; Catoni, Vincenzo; Zampetti, Paolo. Hyperbolic trigonometry in two-dimensional space-time geometry. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0508011/