  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 $\frac{\pi}{2\sqrt{3}}$, which is the density of the optimal unit disc
packing. This result is used to obtain a discrete approximation to the Entropy
functional in two dimensional domain.
