Selected Topics in Geometry with Classical Vs. Computer Proving

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World Scientific, 2007 - Mathematics - 239 pages
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.
 

Contents

1 Introduction
1
2 Automatic theorem proving
5
3 Generalization of the formula of Heron
33
4 SimsonWallace theorem
65
5 Transversals in a polygon
91
6 PetrDouglasNeumann theorem
127
7 Geometric inequalities
163
8 Regular polygons
187
9 Miscellaneous
203
Conclusion
225
Bibliography
227
Index
235
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