Coincidences of simplex centers and related facial structures

2004/11/04 by Allan L. Edmonds, Mowaffaq Hajja, Edmonds, Allan L. +3 · 1 citation
Mathematics · #51M20 (Secondary) #52B11 (Primary) #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:51M20 #msc:52B11

paper · pdf · doi:10.48550/arxiv.math/0411093

24 pages

arxiv created 2004/11/04 · arxiv updated 2009/12/01

Abstract

We investigate the geometric properties of simplices in Euclidean d-dimensional space for which two or more of the analogues of the classical triangle centers (including the centroid, circumcenter, incenter, orthocenter or Monge point, and the Fermat-Torricelli point) coincide. We also investigate the geometric significance of the cevian line segments through a given center having the same length. We give a unified presentation, including known results for d=2 and d=3.

Cited by

• Hyperbolic Simplices of Maximal Inradius

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