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Excursions into Combinatorial Geometry

Bag om Excursions into Combinatorial Geometry

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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  • Sprog:
  • Engelsk
  • ISBN:
  • 9783540613411
  • Indbinding:
  • Paperback
  • Sideantal:
  • 440
  • Udgivet:
  • 14. november 1996
  • Størrelse:
  • 155x23x235 mm.
  • Vægt:
  • 663 g.
  • 8-11 hverdage.
  • 10. december 2024
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Beskrivelse af Excursions into Combinatorial Geometry

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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