How many disks with radius 1/2 are needed to cover a disk with radius 1? It certainly cannot be done with less than 5 small disks, and some non-rigorous drawings of mine suggest it can be done with 7 small disks. Can it be done with less?

Slightly more generally, can anybody point me in the direction of any work on covering bounded bodies with disks? Am i right in thinking that covering disks with smaller disks is the most inefficient kind of covering?

circlewithdisks, the distinction being that a circle is a 1D curve, whereas a disk is the 2D region bounded by a circle. $\endgroup$ – Joseph O'Rourke May 25 '12 at 13:26Sphere Packings, Lattices, and Groups[a.k.a.SPLAG, including by the authors] has a few sections on sphere covering. $\endgroup$ – Noam D. Elkies May 25 '12 at 13:41centersmust be included among those 12 points, none of which is the center of the original disk. Rotations yield uncountably many disjoint sets of 12 points with the same property, which gives the desired contradiction. $\endgroup$ – Noam D. Elkies May 25 '12 at 18:47