
Journal for Geometry and Graphics 09 (2005), No. 2, 141153 Copyright Heldermann Verlag 2005 On the SimsonWallace Theorem and its Generalizations Pavel Pech Pedagogical Faculty, University of South Bohemia, Jeronymova 10, Ceske Budejovice, Czech Republic pech@pf.jcu.cz In this contribution we show generalizations of the well known SimsonWallace Theorem into the space. We use methods of commutative algebra which are based on Gröbner basis computations. This method enables to find and to prove such statements which are often very difficult to prove by techniques of synthetic geometry. In order to display geometric objects we use the dynamic geometry software Cabri and the mathematical software Maple. All computations were done by the computer algebra system CoCoA. Keywords: SimsonWallace Theorem, commutative algebra, normal form, Gr\"obner basis, automatic theorem proving, cubic surface. MSC: 51N20; 51M04, 13P10 [ Fulltextpdf (1543 KB)] for subscribers only. 