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?



covering disks with smaller disks
You'll need seven disks with $r=0.5$ to cover a disk with $r=1$. See <http://mathworld.wolfram.com/DiskCoveringProblem.html>.


