本书是由Leo Moser牵头，花赞25年著成，书中包括500余个颇具吸引力的公开问题，理解其中许多问题并不需要太多的准备知识。书中的各章很大程度上内容自含，概述了离散几何，介绍了各个问题的历史细节及最重要的相关结果。 本书可作为参考书，供致力数学研究，热爱美妙数学问题并不遗余力地试图加以解决的那些专业数学家和研究生查阅。 |
| 0.Definitions and Notations 1.Density Problems for Packings and Goverings 1.1 Basic Questions and Defintions 1.2 The Least Econmical Convex Sets for Packing 1.3 The Least Economical Convex Sets for Covering 1.4 How Economical Are the Lattice Arrangemets? 1.5 Packing with Semidisks,and the Role of Symmetry 1.6 Packing Equal Dircles into Squares,Circles,Spheres 1.7 Packing Equal Circles of Squares in a Strip 1.8 The Densest Packing of Spheres 1.9 The Densest Packings of Specific Convex Bodies 1.10 Linking Packing and Covering Denstities 1.11 Sausage Problems and Catastrophes 2.Structural Packing and Covering Problems 2.1 Decomposition of Multiple Packings and Coverings 2.2 Solid and Saturated Packings and Reduced Coverings 2.3 Stable Packins and Coverings 2.4 Kissing and Neighborly Convex Bodies 2.5 Thin Packings with Many Neighbors 2.6 Permeability and Blocking Light Rays 3.Packing and Covering with Homothetic Copies 3.1 Potato Bay Problems 3.2 Covering a Convex Body with Its Homothetic Copies 3.3 Levi-Hadwiger Covering Problem and Illumination 3.4 Covering a Ball by Slabs 3.5 Point Trapping and Impassable Lattice Arrangements 4.Tilling Problems 5.Distance Problem 6.Problems on Repeated Subconfigurations 7.Incidence and Arrangement Problems 8.Problems on Points in Genral Positon 9.Graph Drawings and Geometric Graphs 10.Lattice Point Problems 11.Geometric Inequalities 12.Index |
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