Absolute geometry proofs of two geometric inequalities of Chisini

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Abstract

Two results, proved synthetically in plane Euclidean geometry by Chisini in 1924—stating that: (i) if MAB is an isosceles triangle, with (Formula presented.), inscribed in a circle (Formula presented.), P1 and P2 are two points on (Formula presented.) such that {B, Pi} separates {A, M} for (Formula presented.), and {B, P2} separates {M, P1}, then (Formula presented.), 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)1-6
Number of pages6
JournalJournal of Geometry
DOIs
StateAccepted/In press - Jun 28 2016

ASJC Scopus subject areas

  • Geometry and Topology

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