Abstract
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∼√3n 2/(4π).
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Graham, R.L., Sloane, N.J.A. Penny-packing and two-dimensional codes. Discrete Comput Geom 5, 1–11 (1990). https://doi.org/10.1007/BF02187775
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DOI: https://doi.org/10.1007/BF02187775