Veit>On May 31, 2011, at 11:35 AM, Allan Wechsler wrote: acw> Blah, I answered this just to Henry. I thought of the p-orbitals of> electrons, and some vibrational modes of a circular drum, and was sure there> were simpler examples of symmetry-breaking but couldn't construct one off> the top of my head. ve>Those are actually not examples of "symmetry-breaking" . The degeneracy (in energy/frequency) is just a manifestation of the symmetry, and indicates the system is especially sensitive to perturbations (that typically "break" the symmetry). Here's an example of true symmetry breaking: the ground state of the lithium trimer (three lithium atoms). If we neglect quantum motion of the nuclei, then the ground state shape is an isosceles triangle. 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.) --rwg