Conclusion
We described some on-going work on improving GeoGebra for studying mechanical linkages by using automated reasoning tools. It was presented that automatic derivation of a locus equation, automatic proving and automatic discovery are all well supported in GeoGebra for non-trivial linkages.
Our experience is that the existing tools are already useful to solve various questions, but studying some linkages may result in too heavy computations. We however conclude that these novel tools are ready to be used in classrooms to enrich STEM education.
Finally we emphasize that our efforts are based on an enormous work of many collaborators and other researchers, including experts of algebraic geometry, computer graphics, computer algebra and programming. This on-going work is a cooperation with Francisco Botana and Bernard Parisse.
Tomás Recio and Francisco Botana were partially supported by MINECO/FEDER grant MTM2014-54141-P. The Lego Technic models were constructed with Benedek Kovács's help.
References
- Abánades, M. A., Botana, F., Kovács, Z., Recio, T. and Sólyom-Gecse, C.: Development of automatic reasoning tools in GeoGebra. Software Demonstration at the ISSAC 2016 Conference. 2016.
- Associacione Macchine Mathematiche
- Bryant, J. and Sangwin, C.: How round is your circle? Where engineering and mathematics meet. Princeton, New Jersey: Princeton University Press. 2008.
- Kapovich, M. and Millson, J.: Universality theorem for configuration spaces of planar linkages. Topology, 41(6) p. 1051-1107. 2002.
- Vincent, J.: Dynamic Geometry Software and Mechanical Linkages. In Networking the Learner: Computers in Education, Watson, D. and Andersen, J., Editors. Springer, Boston, MA. p. 423-432. 2002.
- Brinster, I. and Jumbe, J.: Linkage Simulation in Cinderella. 2009.
- Graver, J. E.: Counting on Frameworks. Dolciani Mathematical Expositions 25. ISBN: 978-0-88385-331-3. Mathematical Association of America. 2002.
- Botana, F. and Valcarce, J. A dynamic-symbolic interface for geometric theorem discovery. In: Computers and Education, 38 p. 21-35. 2002.
- Abánades, M. A., Escribano, J. and Botana F.: Remote Symbolic Computation of Loci, presentation at CADGME 2009, Hagenberg-Linz, Austria. 2009.
- Kovács, Z., Recio, T. and Vélez, M. P.: GeoGebra Automated Reasoning Tools. A Tutorial. 2017.
- West, M.: Four-Bar Linkages. 2015.
- Kempe, A. B.: How to draw a straight line: A lecture on linkages. London, Macmillan. 1877.
- Kovács, Z.: Real-time animated dynamic geometry in the classrooms by using fast Gröbner basis computations. In: Mathematics in Computer Science, 11(1). 2017.