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Development of automatic reasoning tools in GeoGebra

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Csilla Sólyom-GecseAuthors Info & Claims

ACM Communications in Computer Algebra, Volume 50, Issue 3

Pages 85 - 88

https://doi.org/10.1145/3015306.3015309

Published: 04 November 2016 Publication History

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Abstract

Much effort has been put into the implementation of automatic proving in interactive geometric environments (e.g. Java Geometry Expert, GeoGebra). The closely related concept of automatic discovery, remains however almost unexplored.

This software presentation will demonstrate our results towards the incorporation of automatic discovery capabilities into GeoGebra, an educational software with tens of millions of users worldwide. As main result, we report on a new command, currently available in the official version, that allows the automatic discovery of loci of points in diagrams defined by implicit conditions. This represents an extension of a previous command, similar in nature, but restricted to loci defined by the standard mover-tracer construction. Our proposal successfully automates the `dummy locus dragging' in dynamic geometry. This makes the cycle conjecturing-checking-proving accessible for general users in elementary geometry.

References

[1]

F. Botana, M. Hohenwarter, P. Janičić, Z. Kovács, I. Petrović, T. Recio, S. Weitzhofer: Automated theorem proving in GeoGebra: Current achievements, Journal of Automated Reasoning 55: pp. 39--59, 2015.

Digital Library

Google Scholar

[2]

S.-C. Chou: `Mechanical Geometry Theorem Proving', in Mathematics and its Applications, D. Reidel Publ. Comp. Dordrecht, 1988.

Digital Library

Google Scholar

[3]

G. Dalzotto and T. Recio: On protocols for the automated discovery of theorems in elementary geometry, Journal of Automated Reasoning 43: pp. 203--236, 2009.

Digital Library

Google Scholar

[4]

D. Kapur: Wu's method and its application to perspective viewing. In: Geometric Reasoning. D. Kapur and J.L. Mundy, eds. The MIT press, Cambridge, Ma., 1989.

Digital Library

Google Scholar

[5]

T. Recio, M.P. Vélez: Automatic discovery of theorems in elementary geometry, Journal of Automated Reasoning 23: pp. 63--82, 1999.

Digital Library

Google Scholar

[6]

T. Recio, M.P. Vélez: `An introduction to automated discovery in geometry through symbolic computation', in Numerical and Symbolic Scientific Computing: Progress and Prospects, (U. Langer and P. Paule, eds.), Springer Series: Texts and Monographs in Symbolic Computation, Vienna, pp. 25--271, 2011.

Google Scholar

[7]

D. Wang: A new theorem discovered by computer prover, Journal of Geometry 36: pp. 173--182, 1989.

Crossref

Google Scholar

[8]

W. Wen-Tsün: `On the decision problem and the mechanization of theorem-proving in elementary geometry', in Automated theorem proving: After 25 years (W. W. Bledsoe and D. W. Loveland, eds.), AMS, Providence, pp. 213--234, 1984.

Google Scholar

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Dana-Picard T(2023)Computer Assisted Proofs and Automated Methods in Mathematics EducationElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.375.2375(2-23)Online publication date: 10-Mar-2023
https://doi.org/10.4204/EPTCS.375.2
Iordan A(2022)Supervised Learning Use to Acquire Knowledge from 2D Analytic Geometry ProblemsRecent Challenges in Intelligent Information and Database Systems10.1007/978-981-19-8234-7_15(189-200)Online publication date: 24-Nov-2022
https://doi.org/10.1007/978-981-19-8234-7_15
Kovács ZRecio TVélez M(2021)Automated reasoning tools in GeoGebra discoveryACM Communications in Computer Algebra10.1145/3493492.349349555:2(39-43)Online publication date: 20-Oct-2021
https://dl.acm.org/doi/10.1145/3493492.3493495
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Published In

cover image ACM Communications in Computer Algebra

ACM Communications in Computer Algebra Volume 50, Issue 3

September 2016

46 pages

ISSN:1932-2232

EISSN:1932-2240

DOI:10.1145/3015306

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 04 November 2016

Published in SIGSAM-CCA Volume 50, Issue 3

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Dana-Picard T(2023)Computer Assisted Proofs and Automated Methods in Mathematics EducationElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.375.2375(2-23)Online publication date: 10-Mar-2023
https://doi.org/10.4204/EPTCS.375.2
Iordan A(2022)Supervised Learning Use to Acquire Knowledge from 2D Analytic Geometry ProblemsRecent Challenges in Intelligent Information and Database Systems10.1007/978-981-19-8234-7_15(189-200)Online publication date: 24-Nov-2022
https://doi.org/10.1007/978-981-19-8234-7_15
Kovács ZRecio TVélez M(2021)Automated reasoning tools in GeoGebra discoveryACM Communications in Computer Algebra10.1145/3493492.349349555:2(39-43)Online publication date: 20-Oct-2021
https://dl.acm.org/doi/10.1145/3493492.3493495
Kovács Z(2021)Two almost-circles, and two real onesMathematics in Computer Science10.1007/s11786-021-00506-3Online publication date: 26-Mar-2021
https://doi.org/10.1007/s11786-021-00506-3
Guan HRao YZhang JCao SQin X(2021)Method for Processing Graph Degeneracy in Dynamic Geometry Based on Domain DesignJournal of Computer Science and Technology10.1007/s11390-021-0095-836:4(910-921)Online publication date: 1-Jul-2021
https://dl.acm.org/doi/10.1007/s11390-021-0095-8
Cai RChen WZhang LChen RGuan HZou Y(2020)Design and Implementation of Parameters-Based 3D Cutting Function for Dynamic Geometry Software2020 The 4th International Conference on Education and Multimedia Technology10.1145/3416797.3416805(117-122)Online publication date: 19-Jul-2020
https://dl.acm.org/doi/10.1145/3416797.3416805
Ladra MPáez-Guillán PRecio T(2020)Dealing with negative conditions in automated proving: tools and challenges. The unexpected consequences of Rabinowitsch’s trickRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas10.1007/s13398-020-00874-8114:4Online publication date: 2-Jul-2020
https://doi.org/10.1007/s13398-020-00874-8
Botana FKovács ZRecio T(2020)A Mechanical GeometerMathematics in Computer Science10.1007/s11786-020-00497-7Online publication date: 20-Nov-2020
https://doi.org/10.1007/s11786-020-00497-7
Cai RRao YWang JGuan HShi XWang Y(2019)NetPadBrowser: An Offline Browser for Web-Based Dynamic Geometric Resources2019 14th International Conference on Computer Science & Education (ICCSE)10.1109/ICCSE.2019.8845489(434-438)Online publication date: Aug-2019
https://doi.org/10.1109/ICCSE.2019.8845489
Kovács ZRecio TVélez M(2019)Reasoning about linkages with dynamic geometryJournal of Symbolic Computation10.1016/j.jsc.2018.12.003Online publication date: Jan-2019
https://doi.org/10.1016/j.jsc.2018.12.003
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