Towards the Automatic Discovery of Theorems in GeoGebra

  • Miguel Abánades
  • Francisco Botana
  • Zoltán Kovács
  • Tomás Recio
  • Csilla Sólyom-Gecse
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9725)


Considerable attention and efforts have been given to the implementation of automatic reasoning tools in interactive geometric environments. Nevertheless, the main goal in such works focused on theorem proving, cf. Java Geometry Expert or GeoGebra. A related issue, automatic discovery, remains almost unexplored in the field of dynamic geometry software.

This extended abstract sketches our initial results towards the incorporation into GeoGebra, a worldwide spread software with tenths of millions of users, of automatic discovery abilities. As a first result, currently available in the official version, we report on a new command allowing the automatic discovery of loci of points in diagrams. Besides the standard mover-tracer locus finding, the approach also deals with loci constrained by implicit conditions. Hence, our proposal successfully automates a kind of bound dragging in dynamic geometry, the ‘dummy locus dragging’. In this way, the cycle of conjecturing-checking-proving will be accessible for general learners in elementary geometry.


Automatic discovery Dynamic geometry GeoGebra Computational algebraic geometry 



First, second and fourth authors partially supported by the Spanish Ministerio de Economía y Competitividad and by the European Regional Development Fund (ERDF), under the Project MTM2014–54141–P.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Miguel Abánades
    • 1
  • Francisco Botana
    • 2
  • Zoltán Kovács
    • 3
  • Tomás Recio
    • 4
  • Csilla Sólyom-Gecse
    • 5
  1. 1.Universidad Rey Juan CarlosMóstolesSpain
  2. 2.Universidad de VigoVigoSpain
  3. 3.The Private University College of Education of the Diocese of LinzLinzAustria
  4. 4.Universidad de CantabriaSantanderSpain
  5. 5.Babeş-Bolyai UniversityCluj-NapocaRomania

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