Penny-packing and two-dimensional codes
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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).
KeywordsGreedy Algorithm Discrete Comput Geom Hexagonal Lattice Optimal Packing Neighboring Element
- 15.Wegner, Über endliche Kreispackungen in der Ebene,Studia Sci. Math. Hungar., to appear.Google Scholar