Three-reflection theorems in the hyperbolic plane

Mario Marchi; Silvia Pianta; Helmut Karzel

doi:10.4399/97888548357199

Three-reflection theorems in the hyperbolic plane

Mario Marchi, Silvia Pianta, Helmut Karzel

Università Cattolica del Sacro Cuore

Risultato della ricerca: Contributo in rivista › Articolo › peer review

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.

Lingua originale	Inglese
pagine (da-a)	127-140
Numero di pagine	14
Rivista	QUADERNI DI MATEMATICA
Volume	Trends in Incidence and Galois Geometries: a Tribute to Giuseppe Tallini (F. Mazzocca, N. Melone and D. Olanda eds.)
DOI	https://doi.org/10.4399/97888548357199
Stato di pubblicazione	Pubblicato - 2009

Keywords

hyperbolic plane
line-reflection

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10.4399/97888548357199

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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.",

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AB - 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.

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KW - line-reflection

KW - hyperbolic plane

KW - line-reflection

UR - http://hdl.handle.net/10807/8029

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DO - 10.4399/97888548357199

M3 - Article

VL - Trends in Incidence and Galois Geometries: a Tribute to Giuseppe Tallini (F. Mazzocca, N. Melone and D. Olanda eds.)

SP - 127

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JO - QUADERNI DI MATEMATICA

JF - QUADERNI DI MATEMATICA

ER -

Three-reflection theorems in the hyperbolic plane

Abstract

Keywords

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