Abstract
Wegner gave a geometric characterization of all so-called Groemer packing of n ≥ 2 unit discs in E 2 that are densest packings of n unit discs with respect to the convex hull of the discs. In this paper we provide a number theoretic characterization of all n satisfying that such a "Wegner packing" of n unit discs exists, and show that the proportion of these n is 23/24 among all natural numbers.
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Boroczky, K., Ruzsa, I. Note on an Inequality of Wegner. Discrete Comput Geom 37, 245–249 (2007). https://doi.org/10.1007/s00454-006-1277-4
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DOI: https://doi.org/10.1007/s00454-006-1277-4