Excursions into combinatorial geometry - V. G. Bolti͡anskiĭ
KORTE INHOUD
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, int...
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Staat: Goed / Bladzijden: 423 / Druk: / Art.nr. : 1cb68d79-a288-4028-b20f-1c4aeb47dd90 / Vindplaats: opslag 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 ...
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 ...
