| Selected Topics in Geometry with Classical vs. Computer Proving Contributor(s): Pech, Pavel (Author) |
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ISBN: 9812709428 ISBN-13: 9789812709424 Publisher: World Scientific Publishing Company OUR PRICE: $108.30 Product Type: Hardcover - Other Formats Published: January 2008 Annotation: Pech (mathematics, U. of South Bohemia) gives readers the basic theories of automatic theorem proving as well as computational methods as he explains topics of elementary geometry. He describes automatic theorem proving, derivation and discovery, then moves the a generalization of the formula of Heron (the area of a polygon and of a cyclic polygon), the Simson-Wallace theorem (including Gergonne's generalization, the generalization of Guzman and generalization to three dimensions), transversals in a polygon (the theorems of Ceva, Menelaus, Euler and Routh), the Peter-Douglas Neumann theorem (including Napoleon's theorem), geometric inequalities, and regular polygons. He closes with a collection of miscellaneous topics, including non-elementary constructions, the theorem of Viviani and the line of Gauss. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Algebraic - Mathematics | Discrete Mathematics |
| Dewey: 516 |
| LCCN: 2007028204 |
| Physical Information: 0.73" H x 6.09" W x 9.23" (1.09 lbs) 252 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This textbook presents various automatic techniques based on Gr bner 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. |