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。
网站首页 软件下载 游戏下载 翻译软件 电子书下载 电影下载 电视剧下载 教程攻略
书名 | 离散几何中的研究问题(影印版)(精)/国外数学名著系列 |
分类 | 科学技术-自然科学-数学 |
作者 | (美)布拉斯 |
出版社 | 科学出版社 |
下载 | ![]() |
简介 | 编辑推荐 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。 目录 0. Definitions and Notations 1. Density Problems for Packings and Coverings 1.1 Basic Questions and Definitions 1.2 The Least Economical Convex Sets for Packing 1.3 The Least Economical Convex Sets for Covering 1.4 How Economical Are the Lattice Arrangements? 1.5 Packing with Semidisks, and the Role of Symmetry 1.6 Packing Equal Circles into Squares, Circles, Spheres 1.7 Packing Equal Circles or Squares intrip 1.8 The Densest Packing of Spheres 1.9 The Densest Packings of Specific Convex Bodies 1.10 Linking Packing and Covering Densities 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 Packings 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 Bag Problems 3.2overingonvex Body with Its Homothetic Copies 3.3 Levi-Hadwiger Covering Problem and Illumination 3.4 Coveringall by Slabs 3.5 Point Trapping and Impassable Lattice Arrangements 4.Tiling Problems 4.1 Tiling the Plane with Congruent Regions 4.2 Aperiodic Tilings and Tilings with Fivefold Symmetry 4.3 Tiling Space with Polytopes 5.Distance Problems 5.1 The Maximum Number of Unit Distances in the P1ane 5.2 The Number of Equal Distances in Other Spaces 5.3 The Minimum Number of Distinct Distances in the P1an 5.4 The Number of Distinct Distances in Other Spaces 5.5 Repeated Distances in Point Sets in General Position 5.6 Repeated Distances in Point Sets in Convex Position 5.7 Frequent Small Distances and Touching Pairs 5.8 Frequent Large Distances 5.9 Chromatic Number of Unit—Distance Graphs 5.10 Further Problems on Repeated Distances 5.11 Integral or Rational Distances 6.Problems on Repeated Subconfigurations 6.1 Repeated Simplices and Other Patterns 6.2 Repeated Directions,Angles,Areas 6.3 Euclidean Ramsey Problems. 7. Incidence and Arrangement Problems 7.1 The Maximum Number of Incidences 7.2 Sylvester—Gallai—Type Problems 7.3 Line Arrangements Spanned byoint Set 8.Problems on Points in General Position 8.1 Structure of the Space of Order Types 8.2 Convex Polygons and the Erd6s—Szekeres Problem 8.3 Halving Lines and Related Problems 8.4 Extremal Number of Special Subconfigurations 8.5 Other Problems on Points in General Position 9. Graph Drawings and Geometric Graphs 9.1 Graph Drawings 9.2 Drawing Planar Graphs 9.3 The Crossing Number 9.4 Other Crossing Numbers 9.5 From Thrackles to Forbidden Geometric Subgraphs 9.6 Further Turin-Type Problems 9.7 Ramsey—Type Problems 9.8 Geometric Hypergraphs 10.Lattice Point Problems 10.1 Packing Lattice Points in Subspaces 10.2 Covering Lattice Points by Subspaces 10.3 Sets of Lattice Points Avoiding Other Regularities 10.4 Visibility Problems for Lattice Points 11.Geometric Inequalities 1 1.1 Isoperimetric Inequalities for Polygons and Polytopes 11.2 Heilbronn-Type Problems 11.3 Circumscribed and Inscribed Convex Sets 11.4 Universal Covers 11.5 Approximation Problems 12.Index 12.1 Author Index 12.2 Subject Index |
随便看 |
|
霍普软件下载网电子书栏目提供海量电子书在线免费阅读及下载。