Selected topics in geometry with classical vs. computer proving
著者
書誌事項
Selected topics in geometry with classical vs. computer proving
World Scientific, c2007
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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