Where the Truth Lies (in Automatic Theorem Proving in Elementary Geometry)

  • T. Recio
  • F. Botana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3044)


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.


Theorem Prove Elementary Geometry Dynamic Geometry Automatic Theorem Prove Automate Deduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • T. Recio
    • 1
    • 2
  • F. Botana
    • 1
    • 2
  1. 1.Departamento de Matemáticas, Estadística y ComputaciónUniversidad de CantabriaSantanderSpain
  2. 2.Departamento de Matemática Aplicada IUniversidad de Vigo, Campus A XunqueiraPontevedraSpain

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