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Geometric Etudes in Combinatorial Mathematics 2nd Edition

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Alexander Soifer (Author)
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Alexander Soifer (Author)
5 out of 5 stars 1 customer review
ISBN-13: 978-0387754697
ISBN-10: 0387754695
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Product Details

  • Paperback: 264 pages
  • Publisher: Springer; 2nd edition (June 29, 2010)
  • Language: English
  • ISBN-10: 0387754695
  • ISBN-13: 978-0387754697
  • Product Dimensions: 6.1 x 0.7 x 9.2 inches
  • Shipping Weight: 15.2 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #3,044,033 in Books (See Top 100 in Books)

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2 of 3 people found the following review helpful
A smorgasbord of geometry problems with solutions
By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on July 24, 2012
Format: Paperback
Certain areas of geometry are of particular interest to recreational mathematicians and amateurs because the topics and results are extremely visual and in many ways intuitively clear. By restricting the complexity, some of the problems can even be presented in elementary school classes. For example simple problems of filling a figure with polyominoes can be put forward as a challenge for children in elementary school. Finally, the solutions of the problems and even the concepts behind the proofs can be understood once they are displayed.
Boltyanski and Soifer cover some areas of geometry using a large number of figures, the presentation of problems and theorems and solutions to the problems and proofs of the theorems. The first chapter covers tiling rectangular surfaces using polyominoes of various types and the definition of rectangular is extended to include surfaces such as a cylinder and Mobius strip. The pigeonhole principle is introduced in chapter 2 and is used to prove several results concerning the coverage of a geometric figure.
Chapter 3 deals with graphs, the emphasis is on planar graphs, but some three-dimensional structures are included. The fourth and final chapter deals with convex figures, how they can be decomposed into smaller figures, how they can be illuminated by abstract beams of light and theorems such as the Helly Theorem regarding families of convex figures.
The level of difficulty of the theorems and problems presented in this book varies wildly from section to section and there is no overall unifying theme. Nevertheless, the authors have developed an interesting and challenging survey of some areas of geometry and present a small number of unsolved problems for the determined reader to at least attempt to understand and solve.
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