Where the truth lies (in automatic theorem proving in elementary geometry)

Abstract

In this paper we use a new integrated theorem prover (GDI), codeveloped by the second author, to discuss a geometric result due to Maclane, the 83 theorem, which has been declared to be true, according some authors, while other claim it is false. Our approach is based in Gröbner bases computations and illustrates the controversial concept of truth in the algebraic automatic theorem proving model, as well as some of the new features provided by GDI. The potential applications to computer graphics of the idea behind these rather unique features, are also briefly discussed. © Springer-Verlag 2004.