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A dynamic-symbolic interface for geometric theorem discovery

Authors:

Francisco Botana,

José L. ValcarceAuthors Info & Claims

Computers & Education, Volume 38, Issue 1-3

Pages 21 - 35

https://doi.org/10.1016/S0360-1315(01)00089-6

Published: 01 January 2002 Publication History

Abstract

This paper describes Discover, a program for learning and teaching geometry with the help of a computer. The program is a dynamic geometry environment that can communicate with Mathematica, using its symbolic capabilities to perform geometric discovery or rediscovery. Discover is specially suited to be used as a learning tool for geometry from the ages of 12 up to University. It permits the replacement of the traditional ruler and compass by electronic substitutes, as in standard dynamic geometry environments. Through its link with the computer algebra software, it enhances the process of conjecturing and proving. The results can be expressed in natural language or through the use of equations. The mathematical methods that Discover uses are sound, although not complete. Despite this last fact, almost all parts of the school curricula in plane geometry can be adequately treated with the program.

References

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Digital Library

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Cited By

Peng XChen QZhang JChen M(2021)Automated Discovery of Geometric Theorems Based on Vector EquationsJournal of Automated Reasoning10.1007/s10817-021-09591-265:6(711-726)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1007/s10817-021-09591-2
Kovács ZRecio TVélez M(2020)Reasoning about linkages with dynamic geometryJournal of Symbolic Computation10.1016/j.jsc.2018.12.00397:C(16-30)Online publication date: 1-Mar-2020
https://dl.acm.org/doi/10.1016/j.jsc.2018.12.003
Botana FRecio T(2017)Computing envelopes in dynamic geometry environmentsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-016-9500-380:1(3-20)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s10472-016-9500-3
Show More Cited By

Index Terms

A dynamic-symbolic interface for geometric theorem discovery
1. Applied computing
  1. Education
    1. Computer-assisted instruction
  2. Physical sciences and engineering
    1. Mathematics and statistics

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Published In

cover image Computers & Education

Computers & Education Volume 38, Issue 1-3

January 2002

293 pages

ISSN:0360-1315

Issue’s Table of Contents

Publisher

Elsevier Science Ltd.

United Kingdom

Publication History

Published: 01 January 2002

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Cited By

Peng XChen QZhang JChen M(2021)Automated Discovery of Geometric Theorems Based on Vector EquationsJournal of Automated Reasoning10.1007/s10817-021-09591-265:6(711-726)Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1007/s10817-021-09591-2
Kovács ZRecio TVélez M(2020)Reasoning about linkages with dynamic geometryJournal of Symbolic Computation10.1016/j.jsc.2018.12.00397:C(16-30)Online publication date: 1-Mar-2020
https://dl.acm.org/doi/10.1016/j.jsc.2018.12.003
Botana FRecio T(2017)Computing envelopes in dynamic geometry environmentsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-016-9500-380:1(3-20)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s10472-016-9500-3
Botana FHohenwarter MJanicic PKovács ZPetrović IRecio TWeitzhofer S(2015)Automated Theorem Proving in GeoGebraJournal of Automated Reasoning10.1007/s10817-015-9326-455:1(39-59)Online publication date: 1-Jun-2015
https://dl.acm.org/doi/10.1007/s10817-015-9326-4
Botana FKovács Z(2015)A Singular web service for geometric computationsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-014-9438-274:3-4(359-370)Online publication date: 1-Aug-2015
https://dl.acm.org/doi/10.1007/s10472-014-9438-2
Kovács Z(2014)The Relation Tool in GeoGebra 5Revised Selected Papers of the 10th International Workshop on Automated Deduction in Geometry - Volume 920110.1007/978-3-319-21362-0_4(53-71)Online publication date: 9-Jul-2014
https://dl.acm.org/doi/10.1007/978-3-319-21362-0_4
Roanes-Lozano Evan Labeke NRoanes-Macías E(2010)Connecting the 3D DGS Calques3D with the CAS MapleMathematics and Computers in Simulation10.1016/j.matcom.2009.09.00880:6(1153-1176)Online publication date: 1-Feb-2010
https://dl.acm.org/doi/10.1016/j.matcom.2009.09.008
Janičić P(2010)Geometry Constructions LanguageJournal of Automated Reasoning10.1007/s10817-009-9135-844:1-2(3-24)Online publication date: 1-Feb-2010
https://dl.acm.org/doi/10.1007/s10817-009-9135-8
Quaresma P(2010)Thousands of geometric problems for geometric theorem provers (TGTP)Proceedings of the 8th international conference on Automated Deduction in Geometry10.1007/978-3-642-25070-5_10(169-181)Online publication date: 22-Jul-2010
https://dl.acm.org/doi/10.1007/978-3-642-25070-5_10
Abánades MBotana FEscribano JValcarce J(2007)Using free open source software for intelligent geometric computingProceedings of the 2011 international conference on Computational science and its applications - Volume Part IV10.5555/2029365.2029400(353-367)Online publication date: 20-Jun-2007
https://dl.acm.org/doi/10.5555/2029365.2029400
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