On a paper of dan barbilian

Victor Pambuccian

doi:10.1285/i15900932v29n2p29

On a paper of dan barbilian

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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 language	English (US)
Pages (from-to)	29-31
Number of pages	3
Journal	Note di Matematica
Volume	29
Issue number	2
DOIs	https://doi.org/10.1285/i15900932v29n2p29
State	Published - Dec 1 2009

Keywords

Absolute geometry
Hilbert geometry
The Möbius-Pompeiu inequality

ASJC Scopus subject areas

Mathematics(all)

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On a paper of dan barbilian

Abstract

Keywords

ASJC Scopus subject areas

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