Abstract
The axiomatic presentation of geometry fills the gap between formal logic and our spatial intuition. The study of geometry is, and will always be, very important for a mathematical practitioner. GCLCprover, an automatic theorem prover (ATP) integrated with dynamic geometry software (DGS) gives its user a tool to bridge his/her spatial intuition with formal, Euclidean geometry proofs. GeoThms, a system consisting of the mentioned programs and a database geoDB, provides a framework for exploring geometrical knowledge. A GeoThms user can browse through a list of available geometric problems, their statements, illustrations, and proofs. He/she can also interactively produce new geometrical constructions, theorems, and proofs and add new results to the existing ones. GeoThms framework provides an environment suitable for new ways of studying and teaching geometry at different levels. GeoThms also provides a system for storing mathematical knowledge (in a explicit, declarative form) — not only theorem statements, but also their (automatically generated) proofs and corresponding illustrations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bertot, Y., Guilhot, F., Pottier, L.: Visualizing geometrical statements with geoview (2004), http://www-sop.inria.fr/lemme/geoview/geoview.ps
Botana, F., Valcarce, J.L.: A dynamic-symbolic interface for geometric theorem discovery. Computers and Education 38, 21–35 (2002)
Chou, C.C., Gao, X.S., Zhang, J.Z.: Automated production of traditional proofs for constructive geometry theorems. In: Eighth Annual IEEE Symposium on Logic in Computer Science (1993)
Chou, S.-C., Gao, X.-S., Zhang, J.-Z.: Automated generation of readable proofs with geometric invariants, I. multiple and shortest proof generation. Journal of Automated Reasoning 17, 325–347 (1996)
DIMACS. Satisfiability suggested format, ftp://dimacs.rutgers.edu/pub/challenge/satisfiability/doc/satformat.tex
Djorić, M., Janičić, P.: Constructions, instructions, interactions. Teaching Mathematics and its Applications 23(2), 69–88 (2004)
Hoos, H.H., Stützle, T.: Satlib: An online resource for research on sat. In: Proceedings of SAT 2000, IOS Press, Amsterdam (2000), SATLIB is available online at: www.satlib.org
Janičić, P., Trajković, I.: WinGCLC — a Workbench for Formally Describing Figures. In: Proceedings of the 18th Spring Conference on Computer Graphics (SCCG 2003), Budmerice, Slovakia, April, 24-26 2003, pp. 251–256. ACM Press, New York (2003)
Kortenkamp, U., Richter-Gebert, J.: Using automatic theorem proving to improve the usability of geometry software. In: Proceedings of the Mathematical User-Interfaces Workshop 2004 (2004)
Lamport, L.: LaTeX: A Document Preparation System, 2nd edn. Addison-Wesley Publishing Company, Reading (1994)
Marić, F., Janičić, P.: smt-lib in xml clothes. In: Proceedings of Workshop Pragmatics of Decision Procedures in Automated Reasoning (PDPAR-2004) (2004)
Matsuda, N., Vanlehn, K.: Gramy: A geometry theorem prover capable of construction. Journal of Automated Reasoning 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). Technical Report 2006/001, Centre for Informatics and Systems of the University of Coimbra (2006)
Quaresma, P., Pereira, A.: Visualização de construções geométricas. Gazeta de Matemática (to appear)
Ranise, S., Tinelli, C.: The SMT-LIB Format: An Initial Proposal (2003), on-line at: http://goedel.cs.uiowa.edu/smt-lib/
Sutcliffe, G.: The tptp problem library, http://www.cs.miami.edu/~tptp/TPTP/TR/TPTPTR.shtml
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
Quaresma, P., Janičić, P. (2006). Integrating Dynamic Geometry Software, Deduction Systems, and Theorem Repositories. In: Borwein, J.M., Farmer, W.M. (eds) Mathematical Knowledge Management. MKM 2006. Lecture Notes in Computer Science(), vol 4108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11812289_22
Download citation
DOI: https://doi.org/10.1007/11812289_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37104-5
Online ISBN: 978-3-540-37106-9
eBook Packages: Computer ScienceComputer Science (R0)