First steps on using OpenMath to add proving capabilities to standard dynamic geometry systems

Abstract

A prototype for a web application designed to symbolically process locus, proof and discovery tasks on geometric diagrams created with the commercial dynamic geometry systems Cabri, The Geometer’s Sketchpad and Cinderella is presented. The application, named LAD (acronym for Locus-Assertion-Discovery) and thought of as a remote add-on for the considered DGS, follows the Groebner basis method relying on CoCoA and a Mathematica kernel for the involved symbolic computations. From the DGS internal textual representation of a geometric diagram, an OpenMath (i.e. semantic based) description of the requested task is created using the elements in the plangeo OpenMath content dictionaries. A review of the elements included in these CDs is given and two new elements proposed, namely locus and discovery. Everything is finally thoroughly illustrated with examples. LAD is freely accessible at http://nash.sip.ucm.es/LAD/LAD.html .