Automatic discovery of theorems in elementary geometry

Journal of Automated Reasoning

Volumn 23, Issue 1, 1999, Pages 63-82

  Recio, T ^a   Velez M P ^b  

^a UNIVERSITY OF CANTABRIA   (Spain)

^b UNIVERSIDAD ANTONIO DE NEBRIJA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL GEOMETRY; PROBLEM SOLVING;

AUTOMATIC THEOREM PROVING; GROBNER BASIS;

THEOREM PROVING;

EID: 0344210407     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006135322108     Document Type: Article

References (18)

1. Chou, S. C.: Mechanical Geometry Theorem Proving, D. Reidel, 1987.
2. Chou, S. S. and Gao, X. S.: Methods for mechanical geometry formula deriving, in Proceedings ISSAC-90, ACM, New York, 1990, pp. 265-270.
3. Conti, P. and Traverse, C.: A case of automatic theorem proving in Euclidean geometry: The Maclane 83 theorem, in Proceedings AAECC, Paris, 1995.
4. Cox, D., Little, J. and O'Shea, D.: Ideals, Varieties and Algorithms, Undergraduate Texts in Mathematics, Springer-Verlag, 1992.
5. Guergueb, A.: Examples de demostration automatique en gèométrie réelle, Ph. Dissertation, Univ. de Rennes I, 1994.
6. Kapur, D.: Geometry theorem proving using Hilbert's Nullstellensatz, in B. W. Char (ed.), Proc. of the 1986 Symposium on Symbolic and Algebraic Computation, Waterloo, Ont., 1986.
7. Kapur, D.: A refutational approach to theorem proving in geometry, Artif. Intell. 37(1-3) (1988), 61-93.
8. Kapur, D. and Mundy, J. L.: Wu's method and its application to perspective viewing, in D. Kapur and J. L. Mundy (eds.), Geometric Reasoning, The MIT Press, Cambridge, Mass., 1989.
9. Koepf, W.: Gröbner bases and triangles. Internat. J. Comput. Algebra in Math. Education 4(4) (1998), 371-386.
10. Kutzler, B. and Stifter, S.: Automated geometry theorem proving using Buchberger's algorithm, in B. W. Char (ed.), Proc. of the 1986 Symposium on Symbolic and Algebraic Computation, Waterloo, Ont., 1986.
11. Laborde, J. M. and Strässer, R.: Cabri Géomètre, a microworld of geometry for guided discovery learning, Zentralblatt für Didaktik der Mathematik 90(5), 171-190.
12. Mainguené, J.: Méthode de Wu, courbes réelles et demostration automatique en Gèométrie, Ph. Dissertation, Univ. de Rennes I, 1994.
13. Recio, T.: Cálcula Simbólico y Geométrico, Editorial Síntesis, Madrid, 1998.
14. Recio, T., Sterk, H. and Vélez, M. P.: Automatic geometry theorem proving, in A. M. Cohen, H. Cuipers, and H. Sterk (eds.), Some Tapas of Computer Algebra, Algorithms and Computations in Math. 4, Springer-Verlag, 1998.
15. Wang, D.: Gröbner bases applied to geometric theorem proving and discovering, in B. Buchberger and F. Winkler (eds.), Gröbner Bases and Applications, London Math. Soc. Lecture Note Series, Cambridge University Press, Cambridge, 1998.
16. Wu, W. T.: On the decision problem and the mechanization of theorem-proving in elementary geometry, Scientia Sinica 21, 159-172 (also in W. W. Bledsoe and D. W. Loveland (eds.), Automated Theorem Proving: After 25 Years, American Mathematical Society, Providence, 1984, pp. 213-234).
17. Wu, W. T.: On the decision problem and the mechanization of theorem-proving in elementary geometry, Scientia Sinica 21, 159-172 (also in W. W. Bledsoe and D. W. Loveland (eds.), Automated Theorem Proving: After 25 Years, American Mathematical Society, Providence, 1984, pp. 213-234).
18. Wu, W. T.: Mechanical Theorem Proving in Geometries, Texts and Monographs in Symbolic Computation, Springer-Verlag, Wien, 1994.