Journal for Geometry and Graphics 09 (2005), No. 2, 141--153
Copyright Heldermann Verlag 2005
On the Simson-Wallace 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 Simson-Wallace 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: Simson-Wallace Theorem, commutative algebra, normal form, Gr\"obner basis, automatic theorem proving, cubic surface.
MSC: 51N20; 51M04, 13P10
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