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.
Partially supported by the Spanish MICINN, grant MTM2008-04699-C03-03/MTM.
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Botana, F. (2011). A Symbolic Companion for Interactive Geometric Systems. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds) Intelligent Computer Mathematics. CICM 2011. Lecture Notes in Computer Science(), vol 6824. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22673-1_22
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DOI: https://doi.org/10.1007/978-3-642-22673-1_22
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