Circle packing in regular polygons
Circle packing in regular polygons
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正多边形中的圆堆积
DOI：
10.1063/5.0140644
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
P. Amore
中科院分区：
文献类型：
--
作者：
P. Amore
本文研究了正多边形内大量全等且不相交的圆的堆积问题。我们已经设计了有效的算法，使一个产生配置的N密集包装圆内的矩形多边形，我们已经进行了密集的数值实验跨越几个多边形（最大数量的边被认为是16）和多达200个圆（400个圆的特殊情况下的等边三角形和正六边形）。我们发现的一些构型可能不是填充分数的全局最大值，特别是对于N = 1，由于问题的计算复杂性很大，但尽管如此，它们应该在给定的N下为填充分数提供良好的下限。这是第一次系统地研究正多边形的堆积问题，以前只对等边三角形、正方形和圆形进行过研究。
We study the packing of a large number of congruent and non-overlappingcircles inside a regular polygon. We have devised efficient algorithms thatallow one to generate configurations of N densely packed circles inside aregular polygon and we have carried out intensive numerical experimentsspanning several polygons (the largest number of sides considered herebeing 16) and up to 200 circles (400 circles in the special cases of theequilateral triangle and the regular hexagon) . Some of the configurationsthat we have found possibly are not global maxima of the packing frac-tion, particularly for N ≫ 1, due to the great computational complexityof the problem, but nonetheless they should provide good lower boundsfor the packing fraction at a given N . This is the first systematic numeri-cal study of packing in regular polygons, which previously had only beencarried out for the equilateral triangle, the square and the circle.