Aufbau der hyperbolischen geometrie aus dem Geradenorthogonalitätsbegriff

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6 Scopus citations

Abstract

We present an axiom system for plane hyperbolic geometry in a language with lines as the only individual variables and the binary relation of line-perpendicularity as the only primitive notion. It was made possible by results obtained by K. List [6] and H. L. Skala [15]. A similar axiomatization is possible for n-dimensional hyperbolic geometry with n ≧ 4. We also point out that plane hyperbolic geometry admits a ∀∃-axiomatization in terms of line-perpendicularity alone, an axiomatization we could not find.

Original languageEnglish (US)
Pages (from-to)51-61
Number of pages11
JournalActa Mathematica Hungarica
Volume101
Issue number1-2
DOIs
StatePublished - Oct 1 2003

Keywords

  • Hyperbolic geometry
  • Line-orthogonality

ASJC Scopus subject areas

  • Mathematics(all)

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