Abstract

We point out that the axiomatic analysis of the statement The segments joining a point with the vertices of an equilateral triangle satisfy the (non-strict) triangle inequalities in Barbilian's [1] misses the case in which the sum of the angles in a triangle is greater than 180°. We situate the statement correctly inside absolute geometry. We also point out that [1] contains the first proof that a Hilbert geometry with symmetric perpendicularity must be hyperbolic geometry, a proof commonly attributed to P. J. Kelly and L. J. Paige [5].

Original languageEnglish (US)
Pages (from-to)29-31
Number of pages3
JournalNote di Matematica
Volume29
Issue number2
DOIs
StatePublished - Dec 1 2009

Keywords

  • Absolute geometry
  • Hilbert geometry
  • The Möbius-Pompeiu inequality

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On a paper of dan barbilian'. Together they form a unique fingerprint.

  • Cite this