Abstract
Dynamic geometry tools (e.g., Cinderella, Geometer’s Sketchpad, Cabri, Eukleides) visualise geometric objects, allow interactive work, and link formal, axiomatic nature of geometry (most often — Euclidean) with its standard models (e.g., Cartesian model) and corresponding illustrations. These tools are used in teaching and studying geometry, some of them also for producing digital illustrations. The common experience is that dynamic geometry tools significantly help students to acquire knowledge about geometric objects. However, despite the fact that geometry is an axiomatic theory, most (if not all) of these tools concentrate only on concrete models of some geometric constructions and not on their abstract properties — their properties in deductive terms. The user can vary some initial objects and parameters and test if some property holds in all checked cases, but this still does not mean that the given property is valid.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated production of traditional proofs for constructive geometry theorems. In: Proceedings LICS, June 1993, pp. 48–56. IEEE Computer Society Press, Los Alamitos (1993)
Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated generation of readable proofs with geometric invariants. I. JAR 17, 325–347 (1996)
Djorić, M., Janičić, P.: Constructions, instructions, interactions. Teaching Mathematics and its Applications 23(2), 69–88 (2004)
Janičić, P., Trajković, I.: Wingclc — a workbench for formally describing figures. In: Proceedings of SCCG 2003, ACM Press, USA (2003)
Matsuda, N., van Lehn, K.: Gramy: A geometry theorem prover capable of construction. JAR (32), 3–33 (2004)
Narboux, J.: A decision procedure for geometry in coq. In: Slind, K., Bunker, A., Gopalakrishnan, G.C. (eds.) TPHOLs 2004. LNCS, vol. 3223, Springer, Heidelberg (2004)
Obrecht, C.: Eukleides, http://www.eukleides.org/
Quaresma, P., Janičić, P.: Framework for Constructive Geometry (based on the area method). CISUC Technical Report 2006/001 (2006)
Quaresma, P., Pereira, A.: Visualização de construções geométricas. Gazeta de Matemática (151) (July 2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Janičić, P., Quaresma, P. (2006). System Description: GCLCprover + GeoThms. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_13
Download citation
DOI: https://doi.org/10.1007/11814771_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37187-8
Online ISBN: 978-3-540-37188-5
eBook Packages: Computer ScienceComputer Science (R0)