| Excursions Into Combinatorial Geometry 1997 Edition Contributor(s): Boltyanski, Vladimir (Author), Martini, Horst (Author), Soltan, P. S. (Author) |
|
 |
ISBN: 3540613412 ISBN-13: 9783540613411 Publisher: Springer OUR PRICE: $71.20 Product Type: Paperback Published: November 1996 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Analytic - Mathematics | Combinatorics - Mathematics | Calculus |
| Dewey: 516.13 |
| LCCN: 96026787 |
| Series: Universitext |
| Physical Information: 1.02" H x 6.17" W x 9.34" (1.43 lbs) 423 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Geometry undoubtedly plays a central role in modern mathematics. And it is not only a physiological fact that 80 % of the information obtained by a human is absorbed through the eyes. It is easier to grasp mathematical con- cepts and ideas visually than merely to read written symbols and formulae. Without a clear geometric perception of an analytical mathematical problem our intuitive understanding is restricted, while a geometric interpretation points us towards ways of investigation. Minkowski's convexity theory (including support functions, mixed volu- mes, finite-dimensional normed spaces etc.) was considered by several mathe- maticians to be an excellent and elegant, but useless mathematical device. Nearly a century later, geometric convexity became one of the major tools of modern applied mathematics. Researchers in functional analysis, mathe- matical economics, optimization, game theory and many other branches of our field try to gain a clear geometric idea, before they start to work with formulae, integrals, inequalities and so on. For examples in this direction, we refer to MalJ and B-M 2J. Combinatorial geometry emerged this century. Its major lines of investi- gation, results and methods were developed in the last decades, based on seminal contributions by O. Helly, K. Borsuk, P. Erdos, H. Hadwiger, L. Fe- jes T6th, V. Klee, B. Griinbaum and many other excellent mathematicians. |