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

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

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