Cluster Packaging of Spheres Versus Linear Packaging of Spheres

Authors: Helmut Söllinger

The paper analyses the issue of optimised packaging of spheres of the same size. The question is whether a linear packaging of spheres in the shape of a sausage or a spatial cluster of spheres can minimise the volume enveloping the spheres. There is an assumption that for less than 56 spheres the linear packaging is denser and for 56 spheres the cluster is denser, but the question remains how a cluster of 56 spheres could look like. The paper shows two possible ways to build such a cluster of 56 spheres. The author finds clusters of 59, 62, 65, 66, 68, 69, 71, 72, 74, 75, 76, 77, 78, 79 and 80 spheres - using the same method - which are denser than a linear packaging of the same number and gets to the assumption that all convex clusters of spheres of sufficient size are denser than linear ones.

Comments: 10 Pages. language: German

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Submission history

[v1] 2019-03-01 09:40:43

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