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Computer-Generated Geometry Proofs in a Learning Context

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Proof Technology in Mathematics Research and Teaching

Part of the book series: Mathematics Education in the Digital Era ((MEDE,volume 14))

Abstract

Given its formal, logical, and spatial properties, geometry is well suited to teaching environments that include dynamic geometry systems (DGSs) , geometry automated theorem provers (GATPs), and repositories of geometric problems. These tools enable students to explore existing knowledge in addition to creating new constructions and testing new conjectures. In this chapter, we trace the evolution of current automatic proving technologies, how these technologies are beginning to be used by geometry practitioners in general to validate geometric conjectures and generate proofs with natural language and visual rendering, and foresee their evolution and applicability in an educational setting.

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Notes

  1. 1.

    https://cinderella.de.

  2. 2.

    http://poincare.matf.bg.ac.rs/~janicic/gclc/.

  3. 3.

    https://www.geogebra.org/.

  4. 4.

    http://www.cs.wichita.edu/~ye/.

  5. 5.

    http://argo.matf.bg.ac.rs/?content=downloads.

  6. 6.

    The Pythagoras difference is a generalisation of the Pythagorean equality regarding the three sides of a right triangle, to an expression applicable to any triangle (for a triangle ABC with the right angle at B, it holds that \(\mathcal {P}_{ABC}=0\)).

  7. 7.

    Haralambous, Yannis and Quaresma, Pedro, Geometric Statements as Controlled Hybrid Language Sentences, an Example in preparation.

  8. 8.

    http://hilbert.mat.uc.pt/WebGeometryLab.

  9. 9.

    https://github.com/ivan-z-petrovic/open-geo-prover.

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Authors and Affiliations

  1. University of Coimbra, 3001-501, Coimbra, Portugal

    Pedro Quaresma & Vanda Santos

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  1. Pedro Quaresma
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  2. Vanda Santos
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Correspondence to Pedro Quaresma .

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Editors and Affiliations

  1. Ontario Institute for Studies in Education, University of Toronto, Toronto, ON, Canada

    Gila Hanna

  2. AG Didaktik, Fachbereich 3, Universität Bremen, Bremen, Germany

    David A. Reid

  3. Faculty of Education, Stellenbosch University, Stellenbosch, South Africa

    Michael de Villiers

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Quaresma, P., Santos, V. (2019). Computer-Generated Geometry Proofs in a Learning Context. In: Hanna, G., Reid, D., de Villiers, M. (eds) Proof Technology in Mathematics Research and Teaching . Mathematics Education in the Digital Era, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-030-28483-1_11

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