The elementary geometry of a triangular world with hexagonal circles

Research output: Contribution to journalArticle

2 Scopus citations


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
Issue number1
StatePublished - Apr 7 2008



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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this