Excursions into Combinatorial Geometry

Vladimir Boltyanski

ISBN 10: 3540613412 / ISBN 13: 9783540613411

Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 1996, 1996

Beschreibung

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 440 pp. Englisch.

Bestandsnummer des Verkäufers 9783540613411

Bibliografische Details

• Titel: Excursions into Combinatorial Geometry
• Verlag: Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 1996
• Erscheinungsjahr: 1996
• Sprache: Englisch
• ISBN-10: 3540613412
• ISBN-13: 9783540613411
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 24 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 24 mm
• Gewicht: 663 Gramm

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Inhaltsangabe

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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