3 papers
physics.class-ph2005
Space-time trigonometry and formalization of the "Twin Paradox" for uniform and accelerated motions
Dino Boccaletti, Francesco Catoni, Vincenzo Catoni
The formal structure of the early Einstein's Special Relativity follows the axiomatic deductive method of Euclidean geometry. In this paper we show the deep-rooted relation between…
math-ph2005
Lorentz surfaces with constant curvature and their physical interpretation
Francesco Catoni, Roberto Cannata, Vincenzo Catoni +1
In recent years it has been recognized that the hyperbolic numbers (an extension of complex numbers, defined as z=x+h*y with h*h=1 and x,y real numbers) can be associated to space-…
math-ph2005
Hyperbolic trigonometry in two-dimensional space-time geometry
Francesco Catoni, Roberto Cannata, Vincenzo Catoni +1
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 Euc…