Bill, The server is back up and yes, the solutions for 4, 5, 7, 8, ... disks are examples of symmetry breaking (the radii are not equal in the configurations that maximize the radius sum). Fourteen appears to be the first instance where all the radii are distinct. Since fourteen is the first number where symmetry is completely broken, that would make it my favorite number. My place of work was founded on a principle expressed in fourteen words. Veit On Jun 1, 2011, at 5:30 AM, Bill Gosper wrote:
Veit
Is your five disk packing of the unit disk maximizing sum(radii)
(http://gosper.org/HTMLFiles/5disks.gif) an example of either of
these asymmetries? How about your semisecret fourteen disk solution,
which has no symmetry at all? (http://milou.msc.cornell.edu/images/
seems to be down.)
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