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	Packing, covering and tiling in two-dimensional spaces
	Zong, Chuanming
	2014
关键词	Lattice Metric space Archimedean tiling Penrose tiling Quasicrystal Steiner ratio Tammes problem Spherical code Bin packing Apollonian circle packing APOLLONIAN CIRCLE PACKINGS PLANE CONVEX-BODIES EQUAL CIRCLES BIN-PACKING EQUILATERAL TRIANGLE DENSEST PACKING CLOSEST PACKING APPROXIMATION SCHEMES CONGRUENT CIRCLES ISOHEDRAL TILINGS
英文摘要	Packing, covering and tiling is a fascinating subject in pure mathematics. It mainly deals with arrangement patterns and efficiencies of geometric objects. This subject has a long and rich history, even back to Kepler, Newton, Lagrange and Gauss. Inspired by its applications and with the help of computing methods, in recent years it has become a very active research area in mathematics once again. Most of the fundamental problems in this subject can be characterized as simple sounding but challenging. This subject has important applications in many other areas such as Number Theory, Logic, Complex Analysis, Optimization, Coding Theory, Crystallography, Material Science, Industry, and even Biology. In spite of the long history, many of its key problems are still open, even in the plane. The purpose of this paper is to present a comprehensive review for packing, covering and tiling in the two-dimensional spaces. We will focus on the key problems, the fundamental results, the creative ideas, some important applications, and some significant connections with other areas. (C) 2013 Elsevier GmbH. All rights reserved.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000349739100001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics; SCI(E); 0; ARTICLE; cmzong@math.pku.edu.cn; 4; 297-364; 32
语种	英语
出处	SCI
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157415]
专题	数学科学学院
推荐引用方式 GB/T 7714	Zong, Chuanming. Packing, covering and tiling in two-dimensional spaces. 2014-01-01.

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