Coincidences of simplex centers and related facial structures

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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.
24 pages

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Metric Geometry, 52B11 (Primary), 51M20 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/73107

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0411093
 http://arxiv.org/abs/math/0411093

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arXiv