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SELECTED TOPICS IN GEOMETRY WITH CLASSICAL VS. COMPUTER PROVING

by Pavel Pech (University of South Bohemia, Czech Republic)

Table of Contents (70k)
Preface (57k)
Chapter 1: Introduction (87k)

This textbook presents various techniques of elimination based on Gröbner bases 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 easily be done with a ruler and compass.

Each problem is firstly solved by the method of automatic theorem proving. 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


Readership: Undergraduate and graduate students in mathematics.

252pp Pub. date: Dec 2007
ISBN 978-981-270-942-4
981-270-942-8
US$65 / £35
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Copyright © 2008 World Scientific Publishing Co. All rights reserved.
Updated on 12 May 2008