Hyperbolic trigonometry in two-dimensional space-time geometry

F. Catoni, R. Cannata, V. Catoni, P. Zampetti

Research output: Contribution to journalArticle

19 Citations (Scopus)


By analogy with complex numbers, a system of hyperbolic numbers can be introduced in the same way: {z = x + hy; h2 = 1 x, y ∈ 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 using 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.
Original languageEnglish
Pages (from-to)475 - 492
Number of pages18
JournalNuovo Cimento della Societa Italiana di Fisica B
Issue number5
Publication statusPublished - May 2003
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Catoni, F., Cannata, R., Catoni, V., & Zampetti, P. (2003). Hyperbolic trigonometry in two-dimensional space-time geometry. Nuovo Cimento della Societa Italiana di Fisica B, 118(5), 475 - 492.