Excursions into Combinatorial Geometry

Couverture
Springer Science & Business Media, 14 nov. 1996 - 423 pages
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.
 

Table des matières

I
1
II
6
III
12
IV
15
V
20
VI
27
VII
36
VIII
41
XXVII
177
XXVIII
184
XXIX
188
XXX
198
XXXI
209
XXXIII
227
XXXIV
239
XXXV
255

IX
49
XI
58
XII
65
XIII
74
XIV
81
XV
91
XVI
99
XVII
109
XIX
115
XX
121
XXI
127
XXII
135
XXIII
149
XXIV
154
XXV
163
XXVI
173
XXXVII
275
XXXVIII
288
XXXIX
301
XL
309
XLI
319
XLIII
327
XLIV
333
XLV
339
XLVI
346
XLVII
352
XLVIII
365
XLIX
393
L
411
LI
415
LII
Droits d'auteur

Autres éditions - Tout afficher

Expressions et termes fréquents

Informations bibliographiques