Apologies --- I now realise that my configuration was not symmetrical as claimed! So M/m does have lower bound 2, etc etc. WFL On 10/25/08, Fred lunnon <fred.lunnon@gmail.com> wrote:
On 10/25/08, Dan Asimov <dasimov@earthlink.net> wrote:
By the way, Kevin Buzzard & I just realized that this M/m problem is (trivially) equivalent to the "Penny Problem": --
Given n non-overlapping* unit disks in the plane, what is the smallest R = R(n) for which they can be arranged inside of a disk of radius R ?
I think not.
According to http://mathworld.wolfram.com/CirclePacking.html the optimal packing of the latter type arranges the 6 discs with centres on a regular hexagon, for which M/m = 2.
For the configuration I descibed earlier, M/m = 1.931852 .
WFL