Automatic Verification of Regular Constructions in Dynamic Geometry Systems

  • Predrag Janičić
  • Pedro Quaresma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4869)


We present an application of automatic theorem proving (ATP) in the verification of constructions made with dynamic geometry software (DGS). Given a specification language for geometric constructions, we can use its processor to deal with syntactic errors. The processor can also detect semantic errors — situations when, for a given concrete set of geometrical objects, a construction is not possible. However, dynamic geometry tools do not test if, for a given set of geometrical objects, a construction is geometrically sound, i.e., if it is possible in a general case. Using ATP, we can do this last step by verifying the geometric constructions deductively. We have developed a system for the automatic verification of regular constructions (made within DGSs GCLC and Eukleides), using our ATP system, GCLCprover. This gives a real-world application of ATP in dynamic geometry tools.


Area Method Dynamic Geometry Automatic Theorem Prove Semantic Error Dynamic Geometry Software 
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 2007

Authors and Affiliations

  • Predrag Janičić
    • 1
  • Pedro Quaresma
    • 2
  1. 1.Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 BelgradeSerbia
  2. 2.Department of Mathematics, University of Coimbra, 3001-454 CoimbraPortugal

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