Skip to main content
SpringerLink
Log in

Towards Solving the Dynamic Geometry Bottleneck Via a Symbolic Approach

  • Conference paper
Automated Deduction in Geometry (ADG 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3763))

Included in the following conference series:

Abstract

The goal of this paper is to report on a prototype of a new dynamic geometry software, GDI (Geometría Dinámica Inteligente). We will describe how, apart from being a standard dynamic environment for elementary geometry, GDI addresses some key problems of the dynamic geometry paradigm, by including enhanced tools for loci generation and automatic proving, plus another distinguished feature, namely, a discovery option, allowing the user to find complementary hypotheses for arbitrary statements to become true. The key technique for all these improvements is the development of an automatic “bridge” between the graphic and the algebraic counterparts of the program (calling on an external computer algebra system).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. Bazzotti, L., Dalzotto, G., Robbiano, L.: Remarks on geometric theorem proving. In: Richter-Gebert, J., Wang, D. (eds.) ADG 2000. LNCS (LNAI), vol. 2061, pp. 104–128. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  2. 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)

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  4. Botana, F., Valcarce, J.L.: Automatic determination of envelopes and other derived curves within a graphic environment. Mathematics and Computers in Simulation 67(1–2), 3–13 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. 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

  6. Conti, P., Traverso, C.: Algebraic and semialgebraic proofs: Methods and paradoxes. In: Richter-Gebert, J., Wang, D. (eds.) ADG 2000. LNCS (LNAI), vol. 2061, pp. 83–103. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Dolzmann, A., Sturm, A., Weispfenning, V.: A new approach for automatic theorem proving in real geometry. Journal of Automated Reasoning 21, 357–380 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Gawlick, T.: Towards a theory of visualization by dynamic geometry software. Paradigms, phenomena, principles. Int. Conf. on Mathematical Education 10 (ICME 10). Topic Study Group 16, http://www.icme-organisers.dk/tsg16/papers/Gawlick.theoryofvisDGS.pdf

  9. Gao, X.S., Chou, S.C.: Solving geometric constraint systems. I. A global propagation approach. Computer–Aided Design 30, 47–54 (1998)

    Article  Google Scholar 

  10. Gao, X.S., Chou, S.C.: Solving geometric constraint systems. II. A symbolic approach and decision of Rc–constructibility. Computer–Aided Design 30, 115–122 (1998)

    Article  Google Scholar 

  11. Gao, X.S., Zang, J.Z., Chou, S.C.: Geometry expert. Nine Chapters Publ., Taiwan (1998)

    Google Scholar 

  12. Giering, O.: Affine and projective generalization of Wallace lines. Journal of Geometry and Graphics 1(2), 119–133 (1997)

    MATH  MathSciNet  Google Scholar 

  13. González López, M.J.: Using dynamic geometry software to simulate physical motion. International Journal of Computers for Mathematical Learning 6(2), 127–142 (2001)

    Article  Google Scholar 

  14. de Guzmán, M.: An extension of the Wallace–Simson theorem: projecting in arbitrary directions. American Mathematical Monthly 106(6), 574–580 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  15. Hoffmann, C., Bouma, W., Fudos, I., Cai, J., Paige, R.: A geometric constraint solver. Computer–Aided Design 27, 487–501 (1995)

    MATH  Google Scholar 

  16. Jackiw, N.: The Geometer’s Sketchpad. Key Curriculum Press, Berkeley (1997)

    Google Scholar 

  17. King, J., Schattschneider, D.: Geometry turned on Mathematical Association of America, Washington DC (1997)

    Google Scholar 

  18. Kortenkamp, U.: Foundations of dynamic geometry, Ph.D. Thesis, ETH, Zurich (1999)

    Google Scholar 

  19. Kortenkamp, U., Richter-Gebert, J.: A dynamic setup for elementary geometry. In: Proc. Multimedia Tools for Comunicating Mathematics (MTCM 2000). Springer, Heidelberg (2001)

    Google Scholar 

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

    Google Scholar 

  21. Laborde, J.M.: Some issues raised by the development of implemented dynamic geometry as with Cabri-Geometre. In: Proc. 15th European Workshop on Computational Geometry, pp. 7–19 (1999)

    Google Scholar 

  22. MacLane, S.: Some interpretation of abstract linear dependence in terms of projective geometry. American Journal of Mathematics 58, 236–240 (1936)

    Article  MathSciNet  Google Scholar 

  23. Recio, T.: Cálculo simbólico y geométrico. Síntesis, Madrid (1998)

    Google Scholar 

  24. Recio, T., Botana, F.: Where the truth lies (in automatic geometry theorem proving). In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds.) ICCSA 2004. LNCS, vol. 3044, pp. 761–770. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  25. Recio, T., Sterk, H., Vélez, P.: Project: Automated Geometry theorem proving. In: Cohen, A.M., Cuypers, H., Sterk, H. (eds.) Some Tapas of Computer Algebra (Algorithms and Computations in Mathematics, vol. 4, pp. 276–296. Springer, Berlin (1999)

    Google Scholar 

  26. Recio, T., Vélez, M.P.: Automatic discovery of theorems in elementary geometry. Journal of Automated Reasoning 23, 63–82 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  27. Richard, P.: Raisonnement et stratégies de preuve dans l’enseignement des mathématiques, Peter Lang, Berne (2004)

    Google Scholar 

  28. Richter–Gebert, J., Kortenkamp, U.: The interactive geometry software Cinderella. Springer, Berlin (1999)

    Google Scholar 

  29. 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 

  30. Wang, D., Zhi, L.: Algebraic Factorization Applied to Geometric Problems. In: Proc. Third Asian Symposium on Computer Mathematics (ASCM 1998), pp. 23–36. Lanzhou University Press, Lanzhou (1998)

    Google Scholar 

  31. http://www-calfor.lip6.fr/~wang/GRBib/Welcome.html

Download references

Author information

Authors and Affiliations

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

    Francisco Botana

  2. Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Santander, Spain

    Tomás Recio

Authors
  1. Francisco Botana
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tomás Recio
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, NC 27695, Raleigh, USA

    Hoon Hong

  2. LMIB – SKLSDE – School of Science, Beihang University, 100083, Beijing, China

    Dongming Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Botana, F., Recio, T. (2006). Towards Solving the Dynamic Geometry Bottleneck Via a Symbolic Approach. In: Hong, H., Wang, D. (eds) Automated Deduction in Geometry. ADG 2004. Lecture Notes in Computer Science(), vol 3763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11615798_7

Download citation

  • DOI: https://doi.org/10.1007/11615798_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31332-8

  • Online ISBN: 978-3-540-31363-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation