Penny-packing and two-dimensional codes
Penny-packing and two-dimensional codes
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便士包装和二维码
DOI：
10.1007/bf02187775
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发表时间：
1990
影响因子：
0.8
通讯作者：
N. Sloane
中科院分区：
文献类型：
--
作者：
R. Graham;N. Sloane
我们考虑包装问题n相等的圆（即，以使关于它们的质心的二阶矩U最小。这些填充也是最小能量二维码。根据贪婪算法，每次添加一便士会产生前75便士的唯一包装序列，并且似乎会产生无限多个n值的最佳包装。文中还提出了几种其他的结构，并给出了n ≤500时已知的最佳填料的表。对于大的，U = 3 n ~ 2/（4π）。
We consider the problem of packingn equal circles (i.e., pennies) in the plane so as to minimize the second momentU about their centroid. These packings are also minimal-energy two-dimensional codes. Adding one penny at a time according to the greedy algorithm produces a unique sequence of packings for the first 75 pennies, and appears to produce optimal packings for infinitely many values ofn. Several other conjectures are proposed, and a table is given of the best packings known forn≤500. For largen, U∼√3n2/(4π).