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In this paper we generalize the classical theorem of Thue about the optimalcircular 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 everydisc by a factor of $2$ around its center does not contain any center ofanother disc in the family (notice that this implies that the family of discsis a packing). We show that in this case the density of the given packing is atmost $\frac{\pi}{2\sqrt{3}}$, which is the density of the optimal unit discpacking. This result is used to obtain a discrete approximation to the Entropyfunctional in two dimensional domain.

A generalization of Thue's theorem to packings of non-equal discs, and an application to a discrete approximation of entropy