Skip to main content

Computing Locus Equations for Standard Dynamic Geometry Environments

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 4488)

Abstract

GLI (Geometric Locus Identifier), an open web-based tool to determine equations of geometric loci specified using Cabri Geometry and The Geometer’s Sketchpad, is described. A geometric construction of a locus is uploaded to a Java Servlet server, where two computer algebra systems, CoCoA and Mathematica, following the Groebner basis method, compute the locus equation and its graph. Moreover, an OpenMath description of the geometric construction is given. GLI can be efficiently used in mathematics education, as a supplement of the locus functions of the standard dynamic geometry systems. The system is located at http://nash.sip.ucm.es/GLI/GLI.html .

Keywords

  • Interactive geometry
  • Automated deduction
  • Locus
  • OpenMath

References

  1. Autin, B.: Pure and applied geometry with Geometrica. In: Proc. 8th Int. Conf. on Applications of Computer Algebra (ACA 2002), pp. 109–110 (2002)

    Google Scholar 

  2. Botana, F., Valcarce, J.L.: A dynamic-symbolic interface for geometric theorem discovery. Computers and Education 38(1–3), 21–35 (2002)

    CrossRef  Google Scholar 

  3. Botana, F.: Interactive versus symbolic approaches to plane loci generation in dynamic geometry environments. In: Sloot, P.M.A., Tan, C.J.K., Dongarra, J., Hoekstra, A.G. (eds.) ICCS-ComputSci 2002. LNCS, vol. 2330, pp. 211–218. Springer, Heidelberg (2002)

    Google Scholar 

  4. Botana, F., Valcarce, J.L.: A software tool for the investigation of plane loci. Mathematics and Computers in Simulation 61(2), 141–154 (2003)

    CrossRef  MathSciNet  Google Scholar 

  5. Botana, F.: A Web-based intelligent system for geometric discovery. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2657, pp. 801–810. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  6. Botana, F., Recio, T.: Towards solving the dynamic geometry bottleneck via a symbolic approach. In: Hong, H., Wang, D. (eds.) ADG 2004. LNCS (LNAI), vol. 3763, pp. 92–110. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  7. Capani, A., Niesi, G., Robbiano, L.: CoCoA, a system for doing Computations in Commutative Algebra, Available via anonymous ftp from: http://cocoa.dima.unige.it/

  8. Gao, X.S., Zhang, J.Z., Chou, S.C.: Geometry Expert. Taiwan (1998)

    Google Scholar 

  9. http://www.geogebra.at

  10. Jackiw, N.: The Geometer’s Sketchpad v 4.0. Key Curriculum Press, Berkeley (2002)

    Google Scholar 

  11. Laborde, J.M., Bellemain, F.: Cabri Geometry II. Texas Instruments, Dallas (1998)

    Google Scholar 

  12. Miyaji, C., Kimura, H.: Writing a graphical user interface for Mathematica using Mathematica and Mathlink. In: Proc. 2nd Int. Mathematica Symposium (IMS’97), pp. 345–352 (1997)

    Google Scholar 

  13. http://www.openmath.org/

  14. Richter–Gebert, J., Kortenkamp, U.: The Interactive Geometry Software Cinderella. Springer, Berlin (1999)

    Google Scholar 

  15. Roanes–Lozano, E., Roanes–Macías, E., Villar, M.: A bridge between dynamic geometry and computer algebra. Mathematical and Computer Modelling 37(9–10), 1005–1028 (2003)

    MATH  CrossRef  Google Scholar 

  16. Schumann, H.: A dynamic approach to ‘simple’ algebraic curves. Zentralblatt für Didaktik der Mathematik 35(6), 301–316 (2003)

    CrossRef  Google Scholar 

  17. Wang, D.: GEOTHER: A geometry theorem prover. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 166–170. Springer, Heidelberg (1996)

    Google Scholar 

  18. http://www.wolfram.com/products/webmathematica/index.html

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this paper

Cite this paper

Botana, F., Abánades, M.A., Escribano, J. (2007). Computing Locus Equations for Standard Dynamic Geometry Environments. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2007. ICCS 2007. Lecture Notes in Computer Science, vol 4488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72586-2_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72586-2_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72585-5

  • Online ISBN: 978-3-540-72586-2

  • eBook Packages: Computer ScienceComputer Science (R0)