Euler’s inequality in absolute geometry

Victor Pambuccian, Celia Schacht

Research output: Contribution to journalArticle

Abstract

Two results are proved synthetically in Hilbert’s absolute geometry: (i) of all triangles inscribed in a circle, the equilateral one has the greatest area; (ii) of all triangles inscribed in a circle, the equilateral one has the greatest radius of the inscribed circle (which amounts, in the Euclidean case, to Euler’s inequality R≥ 2 r)..

Original languageEnglish (US)
Article number8
JournalJournal of Geometry
Volume109
Issue number1
DOIs
StatePublished - Apr 1 2018

Fingerprint

Equilateral
Triangle
Circle
Incircle or inscribed circle
Euclidean
Radius

Keywords

  • Absolute plane geometry
  • Area
  • Euler’s inequality
  • Optimization

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Euler’s inequality in absolute geometry. / Pambuccian, Victor; Schacht, Celia.

In: Journal of Geometry, Vol. 109, No. 1, 8, 01.04.2018.

Research output: Contribution to journalArticle

Pambuccian, Victor ; Schacht, Celia. / Euler’s inequality in absolute geometry. In: Journal of Geometry. 2018 ; Vol. 109, No. 1.
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