[math-fun] packing circles

Bill Gosper's packing circles in an oval puzzle reminded me of the following packing problem: Find the ellipse of smallest area which can contain n non-overlapping unit disks. This problem is interesting in that even for small n the answer can be non-intuitive. For example, for n = 3, I would have guessed that the best ellipse would be a circle. But it is not. For the best known results up to n = 24 see this page http://www.stetson.edu/~efriedma/cirinel/ at Erich Friedman's packing center. If you find any improvements let Erich know and he will update the page. Jim Buddenhagen