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Selected Topics In Geometry With Classical Vs. Computer ProvingBy Pavel Pech
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This textbook presents various automatic techniques based on Gröbner bases elimination to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects which cannot be easily done with a ruler and compass.
Each problem is firstly solved by an automatic theorem proving method. Secondly, problems are solved classically without using computer where possible so that readers can compare the strengths and weaknesses of both approaches.
Contents: Automatic Theorem Proving; Generalization of the Formula of Heron; Simson Wallace Theorem; Transversals in a Polygon; Petr Douglas Neumann's Theorem; Geometric Inequalities; Regular Polygons.
- Sales Rank: #7029721 in Books
- Published on: 2007-11-12
- Original language: English
- Number of items: 1
- Dimensions: 9.23" h x .73" w x 6.09" l, 1.09 pounds
- Binding: Hardcover
- 252 pages
Review
The selection of the theorems is very nice, making the book quite interesting even to those with no interest in computer-based proofs ... Beside being extremely useful to those who would like to benefit from automatic theorem proving and discovering, the book is also of great interest to anyone interested in geometry, thanks to the beautiful selection of topics it covers. --Zentralblatt MATH
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