A Symbolic Companion for Interactive Geometric Systems

  • Francisco Botana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6824)

Abstract

We consider the problem of enriching a dynamic geometry system with new features from the field of Automated Deduction in Geometry. A prototype based on Sage, sagemath.org, that extends the current capabilities of the interactive environment GeoGebra, geogebra.org, is presented. The prototype provides a deeper knowledge of the different geometric objects in a construction. More precisely, an algebraic symbolic approach based on Groebner Bases is followed to implement a substitute for the numerical approach for property checking and locus plotting used by GeoGebra. As a result the system provides a certified answer in the case of a geometric query or the algebraic equation of the locus in the case of a locus construction. Note that knowing the equation of a locus is necessary to derive new geometric objects from the locus.

References

  1. 1.
    Botana, F.: On the Parametric Representation of Dynamic Geometry Constructions. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds.) ICCSA 2011, Part IV. LNCS, vol. 6785, pp. 342–352. Springer, Heidelberg (2011), http://webs.uvigo.es/fbotana/s11.pdf CrossRefGoogle Scholar
  2. 2.
    Botana, F., Valcarce, J.L.: A Software Tool for the Investigation of Plane Loci. Math. Comput. Simul. 61(2), 139–152 (2003)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Recio, T., Vélez, M.P.: Automatic Discovery of Theorems in Elementary Geometry. J. Autom. Reasoning 23, 63–82 (1999)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Francisco Botana
    • 1
  1. 1.Departamento de Matemática Aplicada IUniversidad de VigoPontevedraSpain

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