General circle packings are arrangements of circles on a given surface such that no two circles overlap except at tangent points. In this paper, we examine the optimal arrangement of circles centered on concentric annuli, in what we term rings. Our motivation for this is two-fold: first, certain industrial applications of circle packing naturally allow for filled rings of circles; second, any packing of circles within a circle admits a ring structure if one allows for irregular spacing of circles along each ring. As a result, the optimization problem discussed herein will be extended in a subsequent paper to a more general setting. With this framework in mind, we present properties of concentric rings that have common points of tangency, the exact solution for the optimal arrangement of filled rings along with its symmetry group, and applications to construction of aluminum-conductor steel reinforced cables.

中文翻译：

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填充圆环的最佳填料

一般圆形填充是在给定表面上的圆形排列，这样除了切点外，没有两个圆形重叠。在本文中，我们研究了以同心环为中心的圆的最佳排列，我们称之为环。我们这样做的动机有两个：首先，圆形填料的某些工业应用自然允许填充圆环；其次，如果允许沿每个环的圆的不规则间距，则在圆内的任何圆的堆积都允许环结构。因此，本文讨论的优化问题将在后续论文中扩展到更一般的设置。考虑到这个框架，我们提出了具有公共切点的同心环的特性，填充环及其对称群的最佳排列的精确解，