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GCLC — A Tool for Constructive Euclidean Geometry and More Than That

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Book cover Mathematical Software - ICMS 2006 (ICMS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4151))

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Abstract

We present gclc/Wingclc — a tool for visualizing geometrical (and not only geometrical) objects and notions, for teaching/studying mathematics, and for producing mathematical illustrations of high quality. gclc uses a language gc for declarative representation of figures and for storing mathematical contents of visual nature in textual form. In gclc, there is a build-in geometrical theorem prover which directly links visual and semantical geometrical information with deductive properties and machine–generated proofs.

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References

  1. Buchberger, B., et al.: Theorema: Towards computer-aided mathematical theory exploration. Journal of Applied Logic (2006)

    Google Scholar 

  2. Cabri site, http://www.cabri.com

  3. Chou, S.C., Gao, X.S., Zhang, J.Z.: Automated production of traditional proofs for constructive geometry theorems. In: Eighth Annual IEEE Symposium on Logic in Computer Science (1993)

    Google Scholar 

  4. Chou, S.C., Gao, X.S., Zhang, J.Z.: Machine Proofs in Geometry. World Scientific, Singapore (1994)

    MATH  Google Scholar 

  5. Chou, S.-C.: Mechanical Geometry Theorem Proving. D.Reidel Publishing Company, Dordrecht (1988)

    MATH  Google Scholar 

  6. Cinderella site, http://www.cinderella.de

  7. Djorić, M., Janičić, P.: Constructions, instructions, interactions. Teaching Mathematics and its Applications 23(2), 69–88 (2004)

    Article  Google Scholar 

  8. Geometer’s Sketchpad site, http://www.keypress.com/sketchpad/

  9. GEX site, http://woody.cs.wichita.edu/gex/7-10/gex.html

  10. Jackiw, N.: The Geometer’s Sketchpad v4.0. Key Curriculum Press, Emeryville (2001)

    Google Scholar 

  11. Janičić, P., Quaresma, P.: System description: Gclcprover + geothms. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS, vol. 4130, pp. 145–150. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Janičić, P.: Zbirka zadataka iz geometrije. Skripta Internacional, Beograd, 1st edition, 6th edition 2005. Collection of problems in geometry (in Serbian) (1997)

    Google Scholar 

  13. Janičić, P., Trajković, I.: WinGCLC — a Workbench for Formally Describing Figures. In: SCCG 2003. ACM Press, New York (2003)

    Google Scholar 

  14. Knuth, D.: TeXBook. Addison Wesley Professional, Reading (1986)

    Google Scholar 

  15. Laborde, J.-M., Strasser, R.: Cabri-géométre: A Microworld of Geometry for Guided Discovery Learning. Zentrablatt Für Didactic der Matematik 22(5) (1990)

    Google Scholar 

  16. Lamport, L.: LaTeX: A Document Preparation System. Addison Wesley Professional, Reading (1994)

    Google Scholar 

  17. Lučić, Z., et al.: Euclid’s Elements, http://www.matf.bg.ac.yu/nastavno/zlucic

  18. Matsuda, N., Vanlehn, K.: Gramy: A geometry theorem prover capable of construction. Journal of Automated Reasoning 32, 3–33 (2004)

    Article  MathSciNet  Google Scholar 

  19. Narboux, J.: A decision procedure for geometry in coq. In: Slind, K., Bunker, A., Gopalakrishnan, G.C. (eds.) TPHOLs 2004. LNCS, vol. 3223, pp. 225–240. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  20. Obrecht, C.: Eukleides, http://www.eukleides.org/

  21. Polthier, K., et al.: JAVA VIEW on-line at: http://javaview.de/

  22. Polthier, K., Khadem, S., Preuss, E., Reitebuch, U.: Publication of interactive visualizations with JavaView. In: Multimedia Tools for Communicating Mathematics. Springer, Heidelberg (2002)

    Google Scholar 

  23. Quaresma, P., Janičić, P.: Framework for the Constructive Geometry. TR2006/001, Center for Informatics and Systems, University of Coimbra (2006)

    Google Scholar 

  24. Quaresma, P., Janičić, P.: Integrating dynamic geometry software, deduction systems, and theorem repositories. In: Borwein, J.M., Farmer, W.M. (eds.) MKM 2006. LNCS, vol. 4108, pp. 280–294. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  25. Richter-Gebert, J., Kortenkamp, U.: Cinderella - The interactive geometry software. Springer, Heidelberg (1999)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11 000, Belgrade, Serbia

    Predrag Janičić

Authors
  1. Predrag Janičić
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Computational Sciences, University of Cantabria, Avda. de los Castros, s/n, E-39005, Santander, Spain

    Andrés Iglesias

  2. Faculty of Science Department of Mathematics, Kobe University, 1-1, Rokkodai, Nada-ku, 657-8501, Kobe, Japan

    Nobuki Takayama

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© 2006 Springer-Verlag Berlin Heidelberg

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Janičić, P. (2006). GCLC — A Tool for Constructive Euclidean Geometry and More Than That. In: Iglesias, A., Takayama, N. (eds) Mathematical Software - ICMS 2006. ICMS 2006. Lecture Notes in Computer Science, vol 4151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11832225_6

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  • DOI: https://doi.org/10.1007/11832225_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38084-9

  • Online ISBN: 978-3-540-38086-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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