The Erdös-Mordell inequality is equivalent to non-positive curvature

Victor Pambuccian

doi:10.1007/s00022-007-1961-4

The Erdös-Mordell inequality is equivalent to non-positive curvature

Victor Pambuccian

Humanities, Arts and Cultural Studies, School of (SHARCS)

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

10 Scopus citations

Abstract

We prove that, in plane absolute geometry, the Erdos-Mordell inequality is equivalent to the statement that the sum of the angles of a triangle is less than or equal to two right angles.

Original language	English (US)
Pages (from-to)	134-139
Number of pages	6
Journal	Journal of Geometry
Volume	88
Issue number	1-2
DOIs	https://doi.org/10.1007/s00022-007-1961-4
State	Published - Mar 1 2008

Keywords

Erdös-Mordell inequality
Hyperbolic geometry
Toponogov's theorem

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s00022-007-1961-4

Cite this

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title = "The Erd{\"o}s-Mordell inequality is equivalent to non-positive curvature",

abstract = "We prove that, in plane absolute geometry, the Erdos-Mordell inequality is equivalent to the statement that the sum of the angles of a triangle is less than or equal to two right angles.",

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The Erdös-Mordell inequality is equivalent to non-positive curvature

Abstract

Keywords

ASJC Scopus subject areas

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