Absolute geometry proofs of two geometric inequalities of Chisini

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1 Scopus citations


Two results, proved synthetically in plane Euclidean geometry by Chisini in 1924—stating that: (i) if MAB is an isosceles triangle, with MA≡MB, inscribed in a circle C, P1 and P2 are two points on C such that {B, Pi} separates {A, M} for i∈ {1 , 2} , and {B, P2} separates {M, P1}, then AP1+ BP1< AP2+ BP2, and (ii) of all triangles inscribed in a given circle the equilateral triangle has the greatest perimeter—are proved inside Hilbert’s absolute geometry.

Original languageEnglish (US)
Pages (from-to)265-270
Number of pages6
JournalJournal of Geometry
Issue number1
StatePublished - Apr 1 2017


  • Absolute plane geometry
  • Primary 51F05
  • Secondary 51M16
  • optimization

ASJC Scopus subject areas

  • Geometry and Topology


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