Fragmente der ebenen hyperbolischen Geometrie

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Abstract

We provide quantifier-free axiomatizations for two fragments of hyperbolic geometry: the hyperbolic geometry of restricted ruler (which can be used to draw the line joining two distinct points, but not to construct the intersection point of two lines), segment-transporter, and set square constructions, and the geometry of BACHMANN's Treffgeradenebenen, and show that both are, in a precise sense, naturally occuring fragments of standard hyperbolic geometry.

Original languageGerman
Pages (from-to)81-95
Number of pages15
JournalPublicationes Mathematicae
Volume65
Issue number1-2
StatePublished - Sep 10 2004

Keywords

  • Geometric construction
  • Hyperbolic geometry
  • Quantifier-free axiomatization

ASJC Scopus subject areas

  • Mathematics(all)

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