Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 2, pp. 491-512 (2005)
Coincidences of simplex centers and related facial structures
Allan L. Edmonds, Mowaffaq Hajja and Horst MartiniDepartment of Mathematics, Indiana University, Bloomington, IN 47405, USA; Department of Mathematics, Yarmouk University, Irbid, Jordan; Faculty of Mathematics, Chemnitz University of Technology, 09107 Chemnitz, Germany
Abstract: This is an investigation of the geometric properties of simplices in Euclidean $d$-dimensional space for which analogues of the classical triangle centers coincide. A presentation of related results is given, partially unifying known results for $d=2$ and $d=3$.
Keywords: barycentric coordinates, centroid, cevian, circumcenter, Cholesky decomposition, Fermat-Torricelli point, Gram matrix, incenter, Monge point, orthocenter, (regular) simplex, simplex center
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Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.