Euler’s inequality in absolute geometry

Victor Pambuccian; Celia Schacht

doi:10.1007/s00022-018-0414-6

Euler’s inequality in absolute geometry

Victor Pambuccian, Celia Schacht

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 language	English (US)
Article number	8
Journal	Journal of Geometry
Volume	109
Issue number	1
DOIs	https://doi.org/10.1007/s00022-018-0414-6
State	Published - Apr 1 2018

Keywords

Absolute plane geometry
Area
Euler’s inequality
Optimization

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s00022-018-0414-6

Cite this

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KW - Optimization

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Euler’s inequality in absolute geometry

Abstract

Keywords

ASJC Scopus subject areas

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