Excursions Into Combinatorial Geometry
Overview
The book deals with the combinatorial geometry of convex bodies in finite-dimensional spaces. A general introduction to geometric convexity is followed by the investigation of d-convexity and H-convexity, and by various applications. Recent research is discussed, for example the three problems from the combinatorial geometry of convex bodies (unsolved in the general case): the Szoekefalvi-Nagy problem, the Borsuk problem, the Hadwiger covering problem. These and related questions are then applied to a new class of convex bodies which is a natural generalization of the class of zonoids: the class of belt bodies. Finally open research problems are discussed. Each section is supplemented by a wide range of exercises and the geometric approach to many topics is illustrated with the help of more than 250 figures.
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Details
- ISBN-13: 9783540613411
- ISBN-10: 3540613412
- Publisher: Springer
- Publish Date: November 1996
- Dimensions: 9.34 x 6.17 x 1.02 inches
- Shipping Weight: 1.43 pounds
- Page Count: 423
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