Skip to main content
SpringerLink
Log in

Real-time Animated Dynamic Geometry in the Classrooms by Using Fast Gröbner Basis Computations

  • Published:
Mathematics in Computer Science Aims and scope Submit manuscript

Abstract

Real-time animation of loci and envelopes in dynamic geometry software may be challenging because of the high amount of heavy symbolic computations being performed continuously. This paper reports on reaching 30 frames per second (FPS) in the desktop application GeoGebra for non-trivial examples for immediate use in classrooms—also 13 FPS is reached in a modern web browser.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abánades, M.Á., Botana, F., Kovács, Z., Recio, T., Sólyom-Gecse, C.: Development of automatic reasoning tools in GeoGebra. ACM Commun. Comput. Algebra 50, 85–88 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abánades, M.Á., Botana, F., Kovács, Z., Recio, T., Sólyom-Gecse, C.: Implicit loci. A GeoGebraBook. http://tube.geogebra.org/m/mbXQuvUV (2016)

  3. Abánades, M.Á., Botana, F., Montes, A., Recio, T.: An algebraic taxonomy for locus computation in dynamic geometry. Comput. Aided Des. 56, 22–33 (2014)

    Article  MATH  Google Scholar 

  4. Bardet, M.: On the complexity of a Gröbner basis algorithm. In: INRIA Seminars. http://algo.inria.fr/seminars/summary/Bardet2002.pdf (2002)

  5. Bertone, C., Chèze, G., Galligo, A.: Modular Las Vegas algorithms for polynomial absolute factorization. J. Symb. Comput. 45(12), 1280–1295 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Birklbauer, P., Drakulić, D.: Implicit curves. In: Second International GeoGebra Conference, Hagenberg, Austria. http://ggbconference2011.pbworks.com/w/file/fetch/44873718/presentation (2011)

  7. Borcherds, M.: Locus Line Equations Demos. A GeoGebraBook. https://www.geogebra.org/b/aUSaUvmp (2016)

  8. Botana, F., Kovács, Z.: Teaching loci and envelopes in GeoGebra. A GeoGebraBook. http://tube.geogebra.org/m/R8nUbEQV (2014)

  9. Botana, F., Kovács, Z.: A Singular web service for geometric computations. Ann. Math. Artif. Intell. 74(3), 359–370 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. Botana, F., Kovács, Z.: New tools in GeoGebra offering novel opportunities to teach loci and envelopes. arXiv:1605.09153 [cs.CG] (2016)

  11. Botana, F., Recio, T.: Computing envelopes in dynamic geometry environments. Ann. Math. Artif. Intell. pp. 1–18 (2016)

  12. Botana, F., Recio, T., Vélez, M. P.: The role of automated reasoning of geometry statements in mathematics instruction. In: Poster at the CERME-10 Conference, Dublin, Ireland (2017)

  13. Boxhofer, E., Huber, F., Lischka, U., Panhuber, B.: MathematiX 1. Veritas Verlag, Linz (2013)

    Google Scholar 

  14. Bright, P.: The Web is Getting its Bytecode: WebAssembly. Ars Technica, Condé Nast (2015)

    Google Scholar 

  15. De Villiers, M.: Exploring Loci on Sketchpad, Pythagoras, 46(47), Mathematical Association of Southern Africa: August/December 1998, pp. 71–73 (1998)

  16. Finkel, R., Bentley, J.L.: Quad trees: a data structure for retrieval on composite keys. Acta Inform 4(1), 1–9 (1974)

    Article  MATH  Google Scholar 

  17. Hašek, R., Kovács, Z., Zahradník, J.: Loci problems in age of reason and their effect on GeoGebra—locus equations and their factorization in GeoGebra. In: International GeoGebra Conference, Budapest, Hungary. http://test.geogebra.org/~kovzol/talks/igi14/bp (2014)

  18. Hohenwarter, M.: GeoGebra: Ein Softwaresystem für dynamische Geometrie und Algebra der Ebene. Master’s thesis, Paris Lodron University, Salzburg, Austria (2002)

  19. Jahn, A.P.: Locus and Trace in Cabri-géomètre: relationships between geometric and functional aspects in a study of transformations. ZDM 34(3), 78 (2002)

    Google Scholar 

  20. Kovács, Z.: Computer based conjectures and proofs in teaching Euclidean geometry. PhD thesis, Johannes Kepler University, Linz, Austria (2015)

  21. Kovács, Z.: RT animated DG in the classrooms by using fast GB. A GeoGebraBook. https://www.geogebra.org/m/Y9pvktxx (2016)

  22. Kovács, Z.: Variations on implicit loci in a triangle. A GeoGebraBook. https://www.geogebra.org/m/gH3b2Vwa (2016)

  23. Kovács, Z.: Implizite Ortslinien in GeoGebra, e-Didaktik conference, Linz. https://www.geogebra.org/m/afpvF72v (2016)

  24. Kovács, Z.: gbt (Gröbner basis tests). A GitHub project. https://github.com/kovzol/gbt (2016)

  25. Kovács, Z.: Envelopes. A GeoGebraBook. https://www.geogebra.org/m/HEyFxCvA (2016)

  26. Kovács, Z., Parisse, B.: Giac and GeoGebra—-improved Gröbner basis computations, In: Computer Algebra and Polynomials, Volume 8942 of the series Lecture Notes in Computer Science, pp. 126–138 (2015)

  27. Losada, R., Recio, T., Valcarce, J. L.: On the automatic discovery of Steiner-Lehmus generalizations, In: Proceedings of ADG’2010, Lecture Notes in Computer Science, Springer, München, pp. 171–174 (2010)

  28. Parisse, B.: About Giac’s Gröbner basis and ideal elimination computation, Presentation at the 22nd Conference on Applications of Computer Algebra Kassel, Germany. http://test.geogebra.org/~kovzol/guests/BernardParisse/aca16-parisse. (2016)

  29. Richter-Gebert, J., Kortenkamp, U.H.: User Manual for the Interactive Geometry Software Cinderella. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

  30. Sendra, J. R., Winkler, F., Perez-Diaz, S.: Rational Algebraic Curves—A Computer Algebra Approach. Springer, Berlin, Heidelberg, ISBN 978-3-540-73724-7 (2008)

  31. Wikipedia contributors, Frame rate, Wikipedia, The Free Encyclopedia. (2016). Accessed 25 Nov 2016

Download references

Author information

Authors and Affiliations

  1. The Private University College of Education of the Diocese of Linz, Salesianumweg 3, 4020, Linz, Austria

    Zoltán Kovács

Authors
  1. Zoltán Kovács
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zoltán Kovács.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kovács, Z. Real-time Animated Dynamic Geometry in the Classrooms by Using Fast Gröbner Basis Computations. Math.Comput.Sci. 11, 351–361 (2017). https://doi.org/10.1007/s11786-017-0308-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11786-017-0308-2

Keywords

Mathematics Subject Classification

Search

Navigation