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Excursions into Combinatorial Geometry (Paperback, 1997 ed.)
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Excursions into Combinatorial Geometry (Paperback, 1997 ed.)
Series: Universitext
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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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