### 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) |
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Pages (from-to) | 29-31 |

Number of pages | 3 |

Journal | Note di Matematica |

Volume | 29 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1 2009 |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Pambuccian, V. (2009). On a paper of dan barbilian.

*Note di Matematica*,*29*(2), 29-31. https://doi.org/10.1285/i15900932v29n2p29