
Journal for Geometry and Graphics 09 (2005), No. 1, 031036 Copyright Heldermann Verlag 2005 The Monge Point and the 3(n+1) Point Sphere of an nSimplex Malgorzata BubaBrzozowa Dept. of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00661 Warsaw, Poland buba@mini.pw.edu.pl The hyperplanes through the centroids of the (n2)dimensional faces of an nsimplex and perpendicular to the respectively opposite 1dimensional edges have a point in common. As a consequence, we define an analogue of the ninepoint circle for any nsimplex. Keywords: Ninepoint circle, Feuerbach circle, Monge point, Euler line, 3(n+1) point sphere, nsimplex, Menelaus theorem, Manheim theorem, Stewart theorem. MSC: 51M04 [ Fulltextpdf (142 KB)] for subscribers only. 