In this paper we study a generalization of the classical non-Euclidean hyperbolic geometry, without assuming for the absolute plane any condition about continuity or the Archimedes' axiom. In this general frame we extend the validity of the fundamental Three-reflection Theorems to the case of any three distinct lines which are pairwise hyperbolic parallel and have a transversal.
Marchi, M., Pianta, S., Karzel, H., Three-reflection theorems in the hyperbolic plane, <<QUADERNI DI MATEMATICA>>, 2010; Trends in Incidence and Galois Geometries: a Tribute to Giuseppe Tallini (F. Mazzocca, N. Melone and D. Olanda eds.) (vol. 19): 127-140. [doi:10.4399/97888548357199] [http://hdl.handle.net/10807/8029]
Three-reflection theorems in the hyperbolic plane
Marchi, Mario;Pianta, Silvia;Karzel, Helmut
2009
Abstract
In this paper we study a generalization of the classical non-Euclidean hyperbolic geometry, without assuming for the absolute plane any condition about continuity or the Archimedes' axiom. In this general frame we extend the validity of the fundamental Three-reflection Theorems to the case of any three distinct lines which are pairwise hyperbolic parallel and have a transversal.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
