Excursions into Combinatorial GeometrySpringer 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 |
393 | |
L | 411 |
415 | |
Autres éditions - Tout afficher
Excursions into Combinatorial Geometry Vladimir Boltyanski,Horst Martini,P.S. Soltan Aperçu limité - 2012 |
Excursions Into Combinatorial Geometry Vladimir Boltyanski,Horst Martini,P. S. Soltan Aucun aperçu disponible - 1996 |
Expressions et termes fréquents
affine hull am+1 apex arbitrary b₁ belt body belt vectors body of constant Borsuk bounded bounded set centrally symmetric closed half-space compact Consequently constant width contained conv H convex body convex body MCR convex cone convex set cross-polytope d-convex denote diam diameter h direction e₁ equality example Exercise exists finite fixing system Furthermore half-space Hence holds homothety inequality integer K₁ l₁ Lemma Let MCR linearly independent M₁ M₂ maximal faces md H minimally dependent vectors Minkowski space n-dimensional normed space obtained one-sided orthogonal outward normal P₁ parallel parallelotope plane polytope positive number problem PROOF Prove real number regular boundary point satisfies the condition segment shows subspace supporting cone supporting hyperplane Theorem translate unit ball vector system vectors e1 vertex vertices zonoid zonotope