Packings of Unequal Circles in a Convex Set

   Abstract. In the Euclidean plane let T be a convex set, and let K ₁ , ..., K _n be a family of n ≥ 2 circles packed into T . We show that the density of each such packing is smaller than , the density of the densest packing of equal circles in the plane, provided the radii of the circles are not too different. This extends a result of G. Fejes Tóth, where T was a polygon with at most six sides.