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Vladimir Boltyanski - Excursions into Combinatorial Geometry
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| Schrijver: | Vladimir Boltyanski |
|---|---|
| Titel: | Excursions into Combinatorial Geometry |
| ISBN: | 9783540613411 |
| Uitgever: | Springer |
| Bijzonderheid: | Staat: Goed / Bladzijden: 423 / Druk: / Art.nr. : 1cb68d79-a288-4028-b20f-1c4aeb47dd90 / Vindplaats: opslag |
| Prijs: |
€ 28,99
€ 4,85
|
| Meer info | Discusses the combinatorial geometry of convex bodies in finite-dimensional spaces. The text includes a general introduction to geometric convexity and investigates d-convexity and H-convexity. Open research problems are considered in detail. 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. |
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