A generalization of Thue’s theorem to packings of non-equal discs, and an application to a discrete approximation of entropy
نویسندگان
چکیده
In this paper we generalize the classical theorem of Thue about the optimal circular disc packing in the plane. We are given a family of circular discs, not necessarily of equal radii, with the property that the inflation of every disc by a factor of 2 around its center does not contain any center of another disc in the family (notice that this implies that the family of discs is a packing). We show that in this case the density of the given packing is at most π 2 √ 3 , which is the density of the optimal unit disc packing.
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