The Feet of the Altitudes of a Simplex

by Arthur Gut, Kantonsschule Zürich-Oerlikon, Switzerland
and Jörg Waldvogel, Seminar for Applied Mathematics, ETH Zürich


We present an elegant algorithm for simultaneously computing all feet F0, F1, ... , Fn of the altitudes of an n-dimensional simplex from the coordinates of its vertices A0, A1, ... , An. The algorithm, which is based on projective geometry and matrix algebra, is valid for every n > 0. Coded in Matlab, it may be expressed by means of three statements using no more than 50 essential characters.

Download the complete paper (7 pages), appeared in "Elemente der Mathematik" 63, 1 (2008), 25 - 29: feet.pdf

Präsentation (22 Folien) "Das Unendliche in der Geometrie: Projektive Räume und homogene Koordinaten",
Fachschaftsweiterbildung Mathematik, Kantonsschule Büelrain, Winterthur
Hörnli-Haus ob Steg ZH, 2. - 3. Juli 2007 buelrain.pdf