Three-reflection theorems in the hyperbolic plane

Silvia Pianta, Mario Marchi, Helmut Karzel

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)127-140
Number of pages14
VolumeTrends in Incidence and Galois Geometries: a Tribute to Giuseppe Tallini (F. Mazzocca, N. Melone and D. Olanda eds.)
Publication statusPublished - 2009


  • hyperbolic plane
  • line-reflection

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