Mechanically proving geometry theorems using a combination of Wu’s method and Collins’ method

Nicholas Freitag McPhee; Shang Ching Chou; Xiao Shan Gao

doi:10.1007/3-540-58156-1_28

Mechanically proving geometry theorems using a combination of Wu’s method and Collins’ method

Nicholas Freitag McPhee, Shang Ching Chou, Xiao Shan Gao

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

6 Scopus citations

Abstract

Wu’s method has been shown to be extremely successful in quickly proving large numbers of geomelxy theorems. However, it is not generally complete for real geomeu’y and is unable to handle inequality problems. Collins’ method is complete for real geometry and is able to handle inequality problems, but is not, at the moment, able to prove some of the more challenging theorems in a practical amount of time and space. This paper presents a combination that is capable of proving theorems beyond the theoretical reach of Wu’s method and the (current) practical reach of Collins’ method. A proof of Pompeiu’s theorem using this combination is given, as well as a list of several other challenging theorems proved using this combination.

Original language	English (US)
Title of host publication	Automated Deduction — CADE-12 - 12th International Conference on Automated Deduction, Proceedings
Editors	Alan Bundy
Publisher	Springer Verlag
Pages	401-415
Number of pages	15
ISBN (Print)	9783540581567
DOIs	https://doi.org/10.1007/3-540-58156-1_28
State	Published - 1994
Event	12th International Conference on Automated Deduction, CADE-12 1994 - Nancy, France Duration: Jun 26 1994 → Jul 1 1994

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	814 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	12th International Conference on Automated Deduction, CADE-12 1994
Country/Territory	France
City	Nancy
Period	6/26/94 → 7/1/94

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1994.

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10.1007/3-540-58156-1_28

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McPhee, N. F., Chou, S. C., & Gao, X. S. (1994). Mechanically proving geometry theorems using a combination of Wu’s method and Collins’ method. In A. Bundy (Ed.), Automated Deduction — CADE-12 - 12th International Conference on Automated Deduction, Proceedings (pp. 401-415). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 814 LNAI). Springer Verlag. https://doi.org/10.1007/3-540-58156-1_28

Mechanically proving geometry theorems using a combination of Wu’s method and Collins’ method. / McPhee, Nicholas Freitag; Chou, Shang Ching; Gao, Xiao Shan.
Automated Deduction — CADE-12 - 12th International Conference on Automated Deduction, Proceedings. ed. / Alan Bundy. Springer Verlag, 1994. p. 401-415 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 814 LNAI).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

McPhee, NF, Chou, SC & Gao, XS 1994, Mechanically proving geometry theorems using a combination of Wu’s method and Collins’ method. in A Bundy (ed.), Automated Deduction — CADE-12 - 12th International Conference on Automated Deduction, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 814 LNAI, Springer Verlag, pp. 401-415, 12th International Conference on Automated Deduction, CADE-12 1994, Nancy, France, 6/26/94. https://doi.org/10.1007/3-540-58156-1_28

McPhee NF, Chou SC, Gao XS. Mechanically proving geometry theorems using a combination of Wu’s method and Collins’ method. In Bundy A, editor, Automated Deduction — CADE-12 - 12th International Conference on Automated Deduction, Proceedings. Springer Verlag. 1994. p. 401-415. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-58156-1_28

McPhee, Nicholas Freitag ; Chou, Shang Ching ; Gao, Xiao Shan. / Mechanically proving geometry theorems using a combination of Wu’s method and Collins’ method. Automated Deduction — CADE-12 - 12th International Conference on Automated Deduction, Proceedings. editor / Alan Bundy. Springer Verlag, 1994. pp. 401-415 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Mechanically proving geometry theorems using a combination of Wu’s method and Collins’ method

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