Skip to main content
Log in

A Web-based Resource for Automatic Discovery in Plane Geometry

  • Published:
International Journal of Computers for Mathematical Learning Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  • Bernat, P. (1994). Calques2.Pont-à-Mousson, France: Topiques Éditions.

    Google Scholar 

  • Bernat, P. and Morinet-Lambert, J. (1996). A new way for visual reasoning in geometry education.In C. Frasson, G. Gauthier, A. Lesgold (Eds), Proc. Intelligent Tutoring Systems ITS'96, Lecture Notes in Computer Science, Vol. 1086 (pp. 448-456).

  • Botana, F. and Valcarce, J.L. (2003). A software tool for the investigation of plane loci.Mathematics and Computers in Simulation 61(2): 141-154.

    Google Scholar 

  • Botana, F. and Valcarce, J.L. (2002). A dynamic-symbolic interface for geometric theorem discovery.Computers and Education 38(1-3): 21-35.

    Google Scholar 

  • Botana, F. and Valcarce, J.L. (2001). Cooperation between a dynamic geometry environment and a computer algebra system for geometric discovery.In V.G. Ganzha, E.W. Mayr and E.V. Vorozhtsov, (Eds), Computer Algebra in Scientific Computing CASC 2001 (pp. 63-74). Berlin: Springer.

    Google Scholar 

  • Buchberger, B. (1985). Groebner bases: An algorithmic method in polynomial ideal theory.In N.K. Bose (Ed.), Multidimensional Systems Theory (pp. 184-232). Dordrecht: Reidel.

    Google Scholar 

  • Capani, A., Niesi, G. and Robbiano, L. CoCoA, a system for doing Computations in Commutative Algebra.Available via anonymous ftp from: cocoa.dima.unige.it

  • Gao, X.S., Zhang, J.Z. and Chou, S.C. (1998). Geometry Expert.Taiwan: Nine Chapters Publ.

    Google Scholar 

  • Goldenberg, E.P. and Cuoco, A. (1998). What is dynamic geometry? In R. Lehrer and D. Chazan (Eds), Designing Learning Environments for Developing Understanding of Geometry and Space (pp. 351-367). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Guzmán, M. (1999). An extension of the Wallace-Simson theorem: Projecting in arbitrary directions.American Mathematical Monthly 106(6): 574-580.

    Google Scholar 

  • Hanna, G. (1997). The ongoing value of proof.Journal Mathematik Didaktik 18(2): 171- 185.

    Google Scholar 

  • Kapur, D. (1988). A refutational approach to geometry theorem proving.Artificial Intelligence 37: 61-94.

    Google Scholar 

  • King, J. and Schattschneider, D. (1997). Geometry Turned On.Washington: MAA.

    Google Scholar 

  • Laborde, J.M. and Straesser, R. (1990). Cabri Géomètre, a microworld of geometry for guided discovery learning.Zentralblatt für Didaktik der Mathematik 22(5): 171-177.

    Google Scholar 

  • NCTM (2000). Principles and Standards for School Mathematics.Reston, VA: NCTM.

    Google Scholar 

  • Nevins, A.J. (1975). Plane geometry theorem proving using forward chaining.Artificial Intelligence 6: 1-23.

    Google Scholar 

  • Recio, T. and Vélez, M.P. (1999). Automatic discovery of theorems in elementary geometry.Journal of Automated Reasoning 23: 63-82.

    Google Scholar 

  • Richter-Gebert, J. and Kortenkamp, U. (1999). The Interactive Geometry Software Cinderella.Berlin: Springer.

    Google Scholar 

  • Roanes, E. (2002). Boosting the geometrical possibilities of dynamic geometry systems and computer algebra systems through cooperation.In M. Borovcnik and H. Kautschitsch (Eds), Technology in Mathematics Teaching (pp. 335-348). Vienna: öbv & hpt.

    Google Scholar 

  • Tall, D. (1997). Cognitive development, representations and proof.In Proc. Justifying and Proving in School Mathematics (pp. 27-38). London: Institute of Education.

    Google Scholar 

  • de Villiers, M. (1997). The role of proof in investigative, computer-based geometry: some personal reflections.In J. King and D. Schattschneider (Eds), Geometry Turned On (pp. 15-24). Washington: MAA.

    Google Scholar 

  • Wu, W.T. (1994). Mechanical Theorem Proving in Geometries.Vienna: Springer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Botana, F. A Web-based Resource for Automatic Discovery in Plane Geometry. International Journal of Computers for Mathematical Learning 8, 109–121 (2003). https://doi.org/10.1023/A:1025636820683

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1025636820683

Keywords

Navigation