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Automated Production of Traditional Proofs for Theorems (1992)
| Venue: | Department of Computer Science, WSU |
| Citations: | 5 - 3 self |
BibTeX
@INPROCEEDINGS{Chou92automatedproduction,
author = {Shang-ching Chou and Xiao-shan Gao and Jing-zhong Zhang},
title = {Automated Production of Traditional Proofs for Theorems},
booktitle = {Department of Computer Science, WSU},
year = {1992},
pages = {109--137}
}
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Abstract
We present a method which can produce traditional proofs for a class of geometry statements whose hypotheses can be described constructively and whose conclusions can be represented by polynomial equations of three kinds of geometry quantities: ratios of line segments, areas of triangles, and Pythagoras differences of triangles. This class covers a large portion of the geometry theorems about straight lines and circles. The method involves the elimination of the constructed points from the conclusion using a few basic geometry propositions. Our program based on the method can produce short and readable proofs of many hard geometry theorems such as Pappus ’ theorem, Simson’s theorem, the Butterfly theorem, Pascal’s theorem, etc. Currently, it has produced proofs of 400 nontrivial theorems entirely automatically. The proofs produced by our program are generally short and readable. This method seems to be the first to produce traditional proofs for hard geometry theorems efficiently.
Keyphrases
traditional proof line segment pascal theorem polynomial equation butterfly theorem geometry quantity readable proof nontrivial theorem straight line many hard geometry theorem geometry statement basic geometry proposition hard geometry pythagoras difference pappus theorem large portion constructed point
