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

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Abstract.

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.

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  1. Department of Integrative Studies, Arizona State University - West campus, P. O. Box 37100, Phoenix, AZ, 85069-7100, U.S.A.

    Victor Pambuccian

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  1. Victor Pambuccian
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Correspondence to Victor Pambuccian.

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Pambuccian, V. The Erdős-Mordell inequality is equivalent to non-positive curvature. J. geom. 88, 134–139 (2008). https://doi.org/10.1007/s00022-007-1961-4

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  • DOI: https://doi.org/10.1007/s00022-007-1961-4

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