The Packing of Equal Circles in a Square
The Packing of Equal Circles in a Square
复制标题
正方形中等圆的堆积
DOI：
10.1080/0025570x.1970.11975991
复制
发表时间：
1970
影响因子：
--
通讯作者：
M. Goldberg
中科院分区：
文献类型：
--
作者：
M. Goldberg
1. 介绍。有许多有趣的极值问题与圆和球的排列有关。Fejes T6th b[1]的书中包含了对这些问题的一个很好的总结。其中包括球体表面的圆的排列，这一问题已由本作者进一步研究。一个最古老的排列问题是在矩形或正方形中排列相等的圆。它今天最常见的应用是包装在一个盒子里的瓶子或罐头。尽管它的历史悠久，用途广泛，但从分析的角度来看，对这个问题所做的工作却很少。最近最好的参考文献是Schaer和Meir的论文[3,4]。他们导出了n~ 9个正方形中n个圆的“最佳”排列。术语“最佳”意味着给定n个圆中最小的正方形，或者给定正方形中圆的最大直径。
1. Introduction. There are many interesting extremal problems associated with the packing of circles and spheres. An excellent summary of these problems is contained in the book by Fejes T6th [1]. These include the packing of circles on the surface of the sphere which has been further investigated by the present author [2].One of the oldest of packing problems is the packing of equal circles in a rectangle or a square. Its most common application today is the packing of bottles or cans in a box. In spite of its antiquity, and its common utility, very little has been done on the problem from an analytical standpoint. The best recent references are the papers by Schaer and Meir [3, 4]. They derived the" best" arrangements for the packing of n circles in a square for n~ 9. The term" best" implies the smallest square for the given n circles, or the largest diameter of the circles for a given square.