Journal for Geometry and Graphics 09 (2005), No. 1, 031--036
Copyright Heldermann Verlag 2005
The Monge Point and the 3(n+1) Point Sphere of an n-Simplex
Dept. of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
The hyperplanes through the centroids of the (n-2)-dimensional faces of an n-simplex and perpendicular to the respectively opposite 1-dimensional edges have a point in common. As a consequence, we define an analogue of the nine-point circle for any n-simplex.
Keywords: Nine-point circle, Feuerbach circle, Monge point, Euler line, 3(n+1) point sphere, n-simplex, Menelaus theorem, Manheim theorem, Stewart theorem.
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