The elementary geometry of a triangular world with hexagonal circles

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Abstract

We provide a collinearity based elementary axiomatics of optimal quantifier complexity ∀∃∀∃ for the geometry inside a triangle and reprove that collinearity cannot be defined in terms of segment congruence, the metric being Hilbert's projective metric.

Original languageEnglish (US)
Pages (from-to)165-175
Number of pages11
JournalBeitrage zur Algebra und Geometrie
Volume49
Issue number1
StatePublished - Apr 7 2008

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Keywords

  • Collinearity
  • Hilbert geometry inside a triangle
  • Quantifier complexity
  • Segment congruence

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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