Skip to main content
View expanded cover

International Conference on Mathematical Knowledge Management

Symposium on the Integration of Symbolic Computation and Mechanized Reasoning

MKM 2007, Calculemus 2007: Towards Mechanized Mathematical Assistants pp 131–145Cite as

First Steps on Using OpenMath to Add Proving Capabilities to Standard Dynamic Geometry Systems

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNAI,volume 4573)

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 .

Keywords

  • Computer Algebra System
  • Dynamic Geometry
  • Automate Theorem Prove
  • Free Point
  • Discovery Task

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-540-73086-6_13
  • Chapter length: 15 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   64.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-73086-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   84.99
Price excludes VAT (USA)
Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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 

  2. 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.J., Zomaya, A.Y. (eds.) ICCS 2003. LNCS, vol. 2657, pp. 801–810. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  3. 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 

  4. Buchberger, B.: Groebner Bases: An algorithmic method in polynomial ideal theory. Multidimensional Systems Theory, D. Reidel Publishing Company, pp. 184–231 (1985)

    Google Scholar 

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

  6. Chou, S.: Mechanical Geometry Theorem Proving. Reidel, Dordrecht Boston (1988)

    MATH  Google Scholar 

  7. Escribano, J., Abánades, M., Valcarce, J., Botana, F.: On Using OpenMath for Representing Geometric Constructions. In: Proc. 6th Int. Workshop on Automated Deduction in Geometry (ADG 2006), pp. 26–30 (2006)

    Google Scholar 

  8. Fateman, N.: A Critique of OpenMath and Thoughts on Encoding Mathematics (January 2001), http://www.cs.berkeley.edu/~fateman

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

    Google Scholar 

  10. http://www.geogebra.at

  11. Jackiw, N.: The Geometer’s Sketchpad v 4. Key Curriculum Press, Berkeley (2002)

    Google Scholar 

  12. http://www.dynamicgeometry.com/javasketchpad

  13. Todd, P.: Geometry Expressions: A Constraint Based Interactive Symbolic Geometry System. Computeralgebra-Rundbrief, vol. 39 (2006)

    Google Scholar 

  14. Hoyles, C., Jones, K.: Proof in Dynamic Geometry Contexts. In: Perspectives on the teaching of Geometry for the 21st Century, pp. 121–128. Kluwer, Dordrecht (1998)

    Google Scholar 

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

    Google Scholar 

  16. http://mathforum.org/kb/

  17. http://www.w3.org/Math/

  18. http://www.openmath.org/

  19. http://www.win.tue.nl/~amc/oz/om/cds/

  20. http://www.riaca.win.tue.nl/products/openmath/lib/index.html

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

    Google Scholar 

  22. 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 

  23. Roozemond, D.A.: Automated proofs using bracket algebra with Cinderella and OpenMath. In: Proc. 9th Rhine Workshop on Computer Algebra (RWCA 2004) (2004)

    Google Scholar 

  24. Wang, D.: GEOTHER: A geometry theorem prover. In: McRobbie, M.A., Slaney, J.K. (eds.) Automated Deduction - Cade-13. LNCS, vol. 1104, Springer, Heidelberg (1996)

    Google Scholar 

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

Download references

Author information

Authors and Affiliations

  1. Ingeniería Técnica en Informática de Sistemas, CES Felipe II (UCM), 28300 Aranjuez, Spain

    Miguel A. Abánades

  2. Departamento de Sistemas Informáticos y Computación, Universidad Complutense de Madrid, 28040 Madrid, Spain

    Jesús Escribano

  3. Departamento de Matemática Aplicada I, Universidad de Vigo, Campus A Xunqueira, 36005 Pontevedra, Spain

    Francisco Botana

Authors
  1. Miguel A. Abánades
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jesús Escribano
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Francisco Botana
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

    Rights and permissions

    Reprints and Permissions

    Copyright information

    © 2007 Springer-Verlag Berlin Heidelberg

    About this paper

    Cite this paper

    Abánades, M.A., Escribano, J., Botana, F. (2007). First Steps on Using OpenMath to Add Proving Capabilities to Standard Dynamic Geometry Systems. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds) Towards Mechanized Mathematical Assistants. MKM Calculemus 2007 2007. Lecture Notes in Computer Science(), vol 4573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73086-6_13

    Download citation

    • DOI: https://doi.org/10.1007/978-3-540-73086-6_13

    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-73083-5

    • Online ISBN: 978-3-540-73086-6

    • eBook Packages: Computer ScienceComputer Science (R0)