Mathematics in Computer Science

, Volume 10, Issue 1, pp 5–25 | Cite as

On the Unavoidable Uncertainty of Truth in Dynamic Geometry Proving

  • Francisco Botana
  • Tomas Recio


The aim of this note is to discuss some issues posed by the emergency of universal interfaces able to decide on the truth of geometric statements. More specifically, we consider a recent GeoGebra module allowing general users to verify standard geometric theorems. Working with this module in the context of Varignon’s theorem, we were driven—by the characteristics of the GeoGebra interface—to perform a quite detailed study of the very diverse fate of attempting to automatically prove this statement, when using two different construction procedures. We highlight the relevance—for the theorem proving output—of expression power of the dynamic geometry interface, and we show that the algorithm deciding about the truth of some—even quite simple—statements can fall into a not true and not false situation, providing a source of confusion for a standard user and an interesting benchmark for geometers interested in discovering new geometric facts.


Dynamic geometry Automated theorem proving GeoGebra Varignon theorem 

Mathematics Subject Classification

Primary 68T15 Secondary 68W30 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Botana F., Kovács Z.: A Singular web service for geometric computations. Ann. Math. Artif. Intell. 74, 359–370 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Botana F., Hohenwarter M., Janičić J., Kovács Z., Petrović I., Recio T., Weitzhofer S.: Automated theorem proving in GeoGebra: current achievements. J. Autom. Reason. 55, 39–59 (2015)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chou S.C.: Mechanical Geometry Theorem Proving. Reidel, Dordrecht (1988)zbMATHGoogle Scholar
  4. 4.
    Dalzotto G., Recio T.: On protocols for the automated discovery of theorems in elementary geometry. J. Autom. Reason. 43, 203–236 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Recio T., Vélez M.P.: Automatic discovery of theorems in elementary geometry. J. Autom. Reason. 23, 63–82 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Recio, T., Sterk, H., Vélez, M.P.: Project: automatic geometry theorem proving. In: Cohen, A., Cuipers, H., Sterk, H. Some Tapas of Computer Algebra. Algorithms and Computations in Mathematics, vol. 4, pp. 276–296. Springer, Heidelberg (1998)Google Scholar

Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Depto. de Matemática Aplicada IUniversity of Vigo, EE ForestalPontevedraSpain
  2. 2.Depto. de Matemáticas, Estadística y ComputaciónUniversity of CantabriaSantanderSpain

Personalised recommendations