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 - 2009

Fingerprint

Lobachevskian geometry
Equilateral triangle
Triangle inequality
Joining
Hilbert
Triangle
Angle

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On a paper of dan barbilian. / Pambuccian, Victor.

In: Note di Matematica, Vol. 29, No. 2, 2009, p. 29-31.

Research output: Contribution to journalArticle

Pambuccian, Victor. / On a paper of dan barbilian. In: Note di Matematica. 2009 ; Vol. 29, No. 2. pp. 29-31.
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