Journal of Geometry

, Volume 88, Issue 1, pp 134–139

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


DOI: 10.1007/s00022-007-1961-4

Cite this article as:
Pambuccian, V. J. geom. (2008) 88: 134. doi:10.1007/s00022-007-1961-4


We prove that, in plane absolute geometry, the Erdős-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.

Mathematics Subject Classification (2000):

51M04 51M09 51F05 03C35 

Key words:

Erdős-Mordell inequality hyperbolic geometry Toponogov’s theorem 

Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of Integrative StudiesArizona State University - West campusPhoenixU.S.A.

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