Abstract
An open web-based tool for automatic discovery in elementary Euclidean geometry, webDiscovery, is described. It is based in recent findings in automatic discovery in geometry. A user-defined geometric construction is uploaded to a Java Servlet server, where two computer algebra systems, CoCoA and Mathematica, return the discovered facts about the construction. webDiscovery can be efficiently used in mathematics education, linkage design and testing and computer aided geometric design. The system can be tested at rosalia.uvigo.es/sdge/web/2D.
Chapter PDF
Similar content being viewed by others
References
Botana, F., Valcarce, J.L.: A dynamic-symbolic interface for geometric theorem discovery. Computers and Education, 38(1–3), 21–35 (2002)
Botana, F.: Interactive versus symbolic approaches to plane loci generation in dynamic geometry environments. Proc. I Int. Workshop on Computer Graphics and Geometric Modelling CGGM’2002, Lecture Notes in Computer Science, 2330, 211–218 (2002)
Botana, F., Valcarce, J.L.: A software tool for the investigation of plane loci. Mathematics and Computers in Simulation, 61(2), 141–154 (2003)
Buchberger, B.: Groebner bases: an algorithmic method in polynomial ideal theory. In N.K. Bose, Multidimensional systems theory, Reidel, Dordrecht, 184–232 (1985)
Capani, A., Niesi, G., Robbiano, L.: CoCoA, a system for doing Computations in Commutative Algebra. Available via anonymous ftp from: ftp://ftp:cocoa.dima.unige.it
Chou, S.C.: Mechanical Geometry Theorem Proving. Reidel, Dordrecht (1988)
Chou, S.C., Gao, X.S., Zhang, J.Z.: Machine Proofs in Geometry. World Scientific, Singapore (1988)
Gao, X.S., Zhang, J.Z., Chou, S.C.: Geometry Expert. Nine Chapters, Taiwan (1998)
Gerlentner, H., Hansen, J.R., Loveland, D.W.: Empirical explorations of the geometry theorem proving machine. Proc. West. Joint Computer Conf., 143–147 (1960)
Guzmán, M.: An extension of the Wallace-Simson theorem: projecting in arbitrary directions. American Mathematical Monthly, 106(6), 574–580 (1999)
Hanna, G.: Proof, explanation and exploration: an overview. Educational Studies in Mathematics, 44(1–2), 5–23 (2002)
Jackiw, N.: The Geometer’s Sketchpad v 4.0. Key Curriculum Press, Berkeley (2002)
Kapur, D.: Using Groebner bases to reason about geometry problems. Journal of Symbolic Computation, 2, 399–408 (1986)
Kapur, D.: A refutational approach to geometry theorem proving. Artificial Intelligence, 37, 61–93 (1988)
Kapur, D., Mundy, J.L.: Wu’s method and its application to perspective viewing. Artificial Intelligence, 37, 15–36 (1988)
King, J., Schattschneider, D.:Geometry Turned On. MAA, Washington (1997)
Laborde, J. M., Bellemain, F.: Cabri Geometry II. Texas Instruments, Dallas (1998)
Laborde, J.M., Straesser, R.: Cabri Géomètre, a microworld of geometry for guided discovery learning. Zentralblatt für Didaktik der Mathematik, 22(5), 171–177 (1990)
Laborde, C.: Dynamic geometry environments as a source of rich learning contexts for the complex activity of proving. Educational Studies in Mathematics, 44(1–2), 151–161 (2002)
Nevins, A.J.: Plane geometry theorem proving using forward chaining. Artificial Intelligence, 6, 1–23 (1975)
Recio, T., Vélez, M. P.: Automatic discovery of theorems in elementary geometry. Journal of Automated Reasoning, 23, 63–82 (1999)
Reiter, R.: A semantically guided deductive system for automatic theorem proving. IEEE Transactions on Computers, C-25(4), 328–334 (1976)
Richter-Gebert, J., Kortenkamp, U.: The Interactive Geometry Software Cinderella. Springer, Berlin (1999)
Valcarce, J.L., Botana, F.: webREX. Available from: http://rosalia.uvigo.es/sdge/web/2D/webREXDemo.zip
Wu, W. T.: Mechanical Theorem Proving in Geometries. Springer, Vienna (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Botana, F. (2003). A Web-Based Intelligent System for Geometric Discovery. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Dongarra, J.J., Zomaya, A.Y., Gorbachev, Y.E. (eds) Computational Science — ICCS 2003. ICCS 2003. Lecture Notes in Computer Science, vol 2657. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44860-8_83
Download citation
DOI: https://doi.org/10.1007/3-540-44860-8_83
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40194-0
Online ISBN: 978-3-540-44860-0
eBook Packages: Springer Book Archive