Abstract
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.
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Notes
- 1.
- 2.
See Java Geometry Expert, JGEX, http://www.cs.wichita.edu/~ye/gex.html, for a paradigmatic example.
- 3.
The command LocusEquation was introduced in GeoGebra version 5.0.213.0, distributed since March 12, 2016. Note that the software has at least one new published version every week.
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Acknowledgment
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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Abánades, M., Botana, F., Kovács, Z., Recio, T., Sólyom-Gecse, C. (2016). Towards the Automatic Discovery of Theorems in GeoGebra. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_5
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