Skip to main content

Using Free Open Source Software for Intelligent Geometric Computing

  • Conference paper
Computational Science and Its Applications - ICCSA 2011 (ICCSA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6785))

Included in the following conference series:

Abstract

This paper describes some examples of fruitful cooperation between geometric software tools (in particular, GeoGebra) and a free open source computer algebra system, Sage (Software for Algebra and Geometry Experimentation). We collect some of our efforts for enhancing mathematics education via technologically rich environments. We show that a math teacher with no specialized programming knowledge can mix widespread resources to get motivating new teaching tools. Furthermore, we explore an exciting but barely used (even known!) characteristic of Sage: its use as a remote kernel. We test it by computing symbolic tasks in a dynamic geometry prototype that are currently out of scope of standard dynamic geometry software. Finally, we illustrate the development of web–based geometric resources by communicating GeoGebra and Sage through Javascript.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    MATH  Google Scholar 

  5. GeoGebra, http://www.geogebra.org

  6. Roanes-Lozano, E., Roanes-Macías, E., Villar, M.: A Bridge between Dynamic Geometry and Computer Algebra. Math. Comput. Model. 37(9-10), 1005–1028 (2003)

    Article  MATH  Google Scholar 

  7. Botana, F., Abánades, M., Escribano, J.: Computing Locus Equations for Standard Dynamic Geometry Environments. In: Shi, Y., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2007. LNCS, vol. 4488, pp. 227–234. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Abánades, M.A., Escribano, J., Botana, F.: First Steps on Using OpenMath to Add Proving Capabilities to Standard Dynamic Geometry Systems. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573, pp. 131–145. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Escribano, J., Botana, F., Abánades, M.A.: Adding Remote Computational Capabilities to Dynamic Geometry Systems. Math. Comput. Simulat. 80, 1177–1184 (2010)

    Article  MathSciNet  Google Scholar 

  10. Abánades, M.A., Botana, F., Escribano, J., Tabera, L.F.: Software matemático libre. Gaceta RSME 12(2), 325–346 (2009)

    MATH  Google Scholar 

  11. Stein, W.A., et al.: Sage Mathematics Software (Version 4.6.0), The Sage Development Team (2010), http://www.sagemath.org

  12. Botana, F., Valcarce, J.L.: A dynamic-symbolic interface for geometric theorem discovery. Comput. Educ. 38(1-3), 21–35 (2002)

    Article  Google Scholar 

  13. Botana, F., Valcarce, J.L.: A software tool for the investigation of plane loci. Math. Comput. Simulat. 61(2,1), 139–152 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Sage server, http://wiki.sagemath.org/SageServer

  15. Lagrange Multipliers (Two Variables), http://ocw.mit.edu/ans7870/18/18.02/f07/tools/LagrangeMultipliersTwoVariables.html

  16. Lagrange-multipliers-applet-interact, https://193.146.36.46:9000/home/pub/4

  17. Apostol, T.M., Mnatsakanian, M.A.: A New Look at the So-Called Trammel of Archimedes. Am. Math. Month. 116(2), 115–133 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Decker, W., Greuel, G.M., Pfister, G., Schönemann, H.: Singular 3-1-1 — A computer algebra system for polynomial computations (2010), http://www.singular.uni-kl.de

  19. EscaleraFlexibleSaturada, https://193.146.36.46:9000/home/pub/5

  20. Capani, A., Niesi, G., Robbiano, L.: CoCoA, a system for doing Computations in Commutative Algebra (1991), http://cocoa.dima.unige.it

  21. Botana, F., Valcarce, J.L.: Automatic determination of envelopes and other derived curves within a graphic environment. Math. Comput. Simulat. 67(1-2), 3–13 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wolfram, S.: Mathematica: a system for doing mathematics by computer, 2nd edn. Addison Wesley Longman Publishing Co., Inc., Redwood City (1991)

    Google Scholar 

  23. Lockwood, E.H.: A Book of Curves. Cambridge University Press, Cambridge (1971)

    Google Scholar 

  24. Template 1, http://nash.sip.ucm.es/Ggb-direct/template1/Ggb-direct-LAD-3PointsAligned.html

  25. GeoGebra JavaScript methods, http://www.geogebra.org/en/wiki/index.php/GeoGebra_Applet_Methods

  26. Template 2, http://nash.sip.ucm.es/Ggb-directPlus/Ggb-directPlus-template-flexible-ladder.html

  27. Simple Sage server, http://www.sagemath.org/doc/reference/sagenb/simple/twist.html

  28. http://www.openmath.org

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Abánades, M.A., Botana, F., Escribano, J., Valcarce, J.L. (2011). Using Free Open Source Software for Intelligent Geometric Computing. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications - ICCSA 2011. ICCSA 2011. Lecture Notes in Computer Science, vol 6785. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21898-9_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-21898-9_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21897-2

  • Online ISBN: 978-3-642-21898-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics