Projective-type axioms for the hyperbolic plane
type: Item
instance of: scholarly article
title: Projective-type axioms for the hyperbolic plane
zbMATH Open document ID: 0780.51015
DOI: 10.1007/BF00181394
author: H. L. Skala
published in: Geometriae Dedicata
publication date: 1993-04-01T00:00:00Z
review text: Karl Menger showed in 1938 that hyperbolic geometry can be developed in terms of the primitive notions of ``point'', ``line'' and ``incidence'' along with postulates that refer only to collinearity, concurrency and the existence of points and lines. However, one of these postulates assumes a special case of the Fundamental Law of Projectivities and so brings in set-theoretical and inductive considerations not present in any of the other axioms. The author shows that the laws of Pappus and Desargues, restricted to cases when the relevant lines intersect, imply the Fundamental Law of Projectivities in the hyperbolic plane. The author thus shows that hyperbolic geometry can be derived solely from configuration postulates.
reviewed by: H.Makiewiecka
Mathematics Subject Classification ID: 51M09
zbMATH DE Number: 147301
zbMATH Keywords: incidence
zbMATH Keywords: hyperbolic geometry
zbMATH Keywords: configuration
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181394
OpenAlex ID: W1998607986
Recommended article: An Axiomatics for Hyperbolic Projective-Metric Planes in Terms of Lines and Orthogonality
Recommended article: Constructive axiomatization of plane hyperbolic geometry
Recommended article: Q5748211
Recommended article: PROJECTIVE HYPERBOLICITY
Recommended article: On some hyperbolic planes from finite projective planes
Recommended article: Projection theorems in hyperbolic space
Recommended article: The simplest axiom system for plane hyperbolic geometry
Recommended article: Hyperbolicity of Projective Hypersurfaces
Recommended article: Q5482811
Recommended article: Constructive Axiomatizations of Plane Absolute, Euclidean and Hyperbolic Geometry
description: scientific article; zbMATH DE number 147301