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The Relation Tool in GeoGebra 5

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Automated Deduction in Geometry (ADG 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9201))

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Abstract

GeoGebra is open source mathematics education software being used in thousands of schools worldwide. Its new version 5 supports automatic geometry theorem proving by using various methods which are already well known, but not widely used in education software. GeoGebra’s new embedded prover system chooses one of the available methods and translates the problem specified by the end user as the input for the selected method, similarly to portfolio solvers. The available methods include Wu’s method, the Buchberger-Kapur method, the Area method and Recio’s exact check method, some of them as embedded algorithms, others as outsourced computations. These methods can also be hidden from end users who are provided with an intuitive graphical user interface, the Relation Tool. Since GeoGebra maintains the development in an open-sourced way by collaborating with the OpenGeoProver, Singular and Giac projects, further enhancements can be expected by a larger community, including implementing other methods, too.

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Notes

  1. 1.

    http://home.gna.org/geoproof/.

  2. 2.

    http://www.mmrc.iss.ac.cn/gex/.

  3. 3.

    One example of a system planned for teaching proofs interactively is Jacques Gressier’s Géométrix, available at http://geometrix.free.fr.

  4. 4.

    http://wiki.geogebra.org/en/Release_Notes_GeoGebra_5.0#New_Command_Line_Arguments.

  5. 5.

    See http://dev.geogebra.org/trac/wiki/TheoremProving for more details. This documentation includes detailed description of the applied methods and the supported constructions and statements for them.

  6. 6.

    For an example, see http://wiki.geogebra.org/en/ProveDetails_Command.

  7. 7.

    See http://www.geogebratube.org/student/b104296 for an example.

  8. 8.

    Degeneracy conditions can be obtained only by two methods at the moment.

  9. 9.

    See http://test.geogebra.org/~kovzol/data/Prove-20150219b/ for a recent report on benchmarking various theorems with the R-Prover based on computations with Singular and Giac, and compared with OGP’s Wu’s method. The full source code of GPP and its benchmarking system are freely available at https://dev.geogebra.org/trac/browser/trunk/geogebra in folders common/src/main/java/org/geogebra/common/kernel/prover/ and test/, respectively.

  10. 10.

    GeoGebra 5 can be downloaded from its official web site http://www.geogebra.org/download.

  11. 11.

    Java method names in the log are obfuscated to ensure faster results and a smaller software package.

  12. 12.

    To obtain exactly the same result, the user needs to force using SingularWS which is deactivated by default in GeoGebra 5. Enabling SingularWS can be performed by using the command line geogebra --singularws=enable:true e.g. on Linux. When SingularWS is disabled, Giac is used to compute the results: here case 2. (a) (iv.) B. (i.e., “possibly generally true”) will be selected.

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Acknowledgments

Ivan Petrović, PhD student of University of Belgrade, the primary author of OGP had a great part in making OGP generally work. Gábor Ancsin was the leader of the HTML5 based experiments in the GeoGebra Team. Michael Borcherds and Zbyněk Konečný helped regularly to find and eliminate bugs during the development. Last but not least, Bernard Parisse kindly helped in improving Giac to be even more robust for Gröbner basis computations.

Bruno Buchberger kindly invited the author of this paper to present a preliminary version of this paper at the RISC Theorema seminar on 9 April 2014. (The slides for that talk are available to download at http://ggb1.idm.jku.at/~kovzol/talks/risc2014-2/.)

Pedro Quaresma and Francisco Botana supported the author to present essential parts of this paper at the ADG 2014 conference on 10 July 2014. (Slides and supplementary materials for this talk can be accessed at http://ggb1.idm.jku.at/~kovzol/talks/adg2014/.)

Author information

Authors and Affiliations

  1. Department of Mathematics Education, Johannes Kepler University, Altenberger Strasse 54, 4040, Linz, Austria

    Zoltán Kovács

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  1. Zoltán Kovács
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Correspondence to Zoltán Kovács .

Editor information

Editors and Affiliations

  1. University of Vigo, Pontevedra, Spain

    Francisco Botana

  2. University of Coimbra, Coimbra, Portugal

    Pedro Quaresma

Appendix

Appendix

1.1 Log Output for Ceva’s Theorem

figure c

1.2 Log Output for Thales’s Circle Theorem

figure d

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Kovács, Z. (2015). The Relation Tool in GeoGebra 5. In: Botana, F., Quaresma, P. (eds) Automated Deduction in Geometry. ADG 2014. Lecture Notes in Computer Science(), vol 9201. Springer, Cham. https://doi.org/10.1007/978-3-319-21362-0_4

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  • DOI: https://doi.org/10.1007/978-3-319-21362-0_4

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