Almost-Tiling the Plane by Ellipses

Let C be a system (finite or infinite) of centrally symmetric convex bodies in IR with disjoint interiors; we call such a C a packing . For a real number ε > 0 and for C ∈ C, we let C denote C enlarged by the factor 1+ ε from its center, that is, C = (1+ ε)(C − c) + c, where c stands for the center of symmetry C. Let us call the closure of the set C \C the ε-ring of C. We call the system C = {C; C ∈ C} the (1 + ε)-enlargement of C.