Towards an Automated Geometer

  • Francisco Botana
  • Zoltán Kovács
  • Tomás Recio
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11110)


We report on preliminary work towards the automated finding of theorems in elementary geometry. The resulting system is being currently implemented on top of GeoGebra, a dynamic geometry system with millions of users at high schools and universities. Our system exploits GeoGebra’s recently added new functionalities concerning automated reasoning tools in geometry. We emphasize that the method for finding geometric properties that are present on a user-provided construction is purely symbolic, thus giving such properties rigorous mathematical certainty. We describe some generalities about the system we are developing, which are illustrated through an example.


Automated discovery Automated theorem proving Computer algebra GeoGebra 



Authors partially supported by the grant MTM2017-88796-P from the Spanish MINECO and the ERDF (European Regional Development Fund).


  1. 1.
    Lenat, D.B.: Automated theory formation in mathematics. Contemp. Math. 29, 287–314 (1984)MathSciNetCrossRefGoogle Scholar
  2. 2.
    de Guzmán, M.: La experiencia de descubrir en geometría. Nivola (2002)Google Scholar
  3. 3.
    Bagai, R., Shanbhogue, V., Żytkow, J.M., Chou, S.C.: Automatic theorem generation in plane geometry. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 415–424. Springer, Heidelberg (1993). Scholar
  4. 4.
    Chou, S.C., Gao, X.S., Zhang, J.Z.: A deductive database approach to automated geometry theorem proving and discovering. J. Autom. Reason. 25, 219–246 (2000)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chen, X., Song, D., Wang, D.: Automated generation of geometric theorems from images of diagrams. Ann. Math. Artif. Intell. 74, 333–358 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Botana, F., Hohenwarter, M., Janicic, P., Kovács, Z., Petrovic, I., Recio, T., Weitzhofer, S.: Automated theorem proving in GeoGebra: current achievements. J. Autom. Reason. 55, 39–59 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Magajna, Z.: OK Geometry. Accessed 3 May 2018
  8. 8.
    The GeoGebra Team: Reference: GeoGebra Apps API. Accessed 10 May 2018
  9. 9.
    Kovács, Z., Parisse, B.: Giac and GeoGebra - improved Gröbner basis computations. In: Gutierrez, J., Schicho, J., Weimann, M. (eds.) Computer Algebra and Polynomials. LNCS, vol. 8942, pp. 126–138. Springer, Cham (2015). Scholar
  10. 10.
    Bright, P.: The web is getting its bytecode: WebAssembly. Condé Nast (2015)Google Scholar
  11. 11.
    Recio, T., Vélez, M.P.: Automatic discovery of theorems in elementary geometry. J. Autom. Reason. 23, 63–82 (1999)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Gao, H., Goto, Y., Cheng, J.: A set of metrics for measuring interestingness of theorems in automated theorem finding by forward reasoning: a case study in NBG set theory. In: He, X. (ed.) IScIDE 2015. LNCS, vol. 9243, pp. 508–517. Springer, Cham (2015). Scholar
  13. 13.
    Botana, F., Kovács, Z., Martínez-Sevilla, A., Recio, T.: Automatically augmented reality with GeoGebra (to appear)Google Scholar
  14. 14.
    Abánades, M., Botana, F., Kovács, Z., Recio, T., Sólyom-Gecse, C.: Development of automatic reasoning tools in GeoGebra. ACM Commun. Comput. Algebr. 50, 85–88 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Francisco Botana
    • 1
  • Zoltán Kovács
    • 2
  • Tomás Recio
    • 3
  1. 1.Department of Applied Mathematics IUniversity of VigoPontevedraSpain
  2. 2.The Private University College of Education of the Diocese of LinzLinzAustria
  3. 3.Universidad de CantabriaSantanderSpain

Personalised recommendations