Absolute geometry proofs of two geometric inequalities of Chisini

Victor Pambuccian

doi:10.1007/s00022-016-0339-x

Absolute geometry proofs of two geometric inequalities of Chisini

Victor Pambuccian

Research output: Contribution to journal › Article

1 Scopus citations

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, P_i} 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 language	English (US)
Pages (from-to)	1-6
Number of pages	6
Journal	Journal of Geometry
DOIs	https://doi.org/10.1007/s00022-016-0339-x
State	Accepted/In press - Jun 28 2016

ASJC Scopus subject areas

Geometry and Topology

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Pambuccian, V. (Accepted/In press). Absolute geometry proofs of two geometric inequalities of Chisini. Journal of Geometry, 1-6. https://doi.org/10.1007/s00022-016-0339-x

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