For best known packings of equal circles in a circle see here http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html On Fri, Feb 19, 2016 at 2:07 PM, Charles Greathouse < charles.greathouse@case.edu> wrote:
Maybe it's obvious, but I'd just like to know if the maximal sum of the radii of n circles in a circle of unit radius approaches its upper bound sqrt(n). (Or have I been caught in the sort of trap that inspired this conversation?)
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Feb 19, 2016 at 9:08 AM, Veit Elser <ve10@cornell.edu> wrote:
On Feb 19, 2016, at 8:48 AM, Fred Lunnon <fred.lunnon@gmail.com>
wrote:
I'm a tad suspicious: are the circle packings on Friedman's page
proved
to be maximal, or are they merely the best known so far? There is no link to any proofs, or key to diameters … WFL
I have a conjecture that the maximum-sum-of-diameters packings have triangulated contact graphs. If that’s true, one could enumerate the graphs and calculate the packing for each one to see which is maximal.
-Veit
http://mathoverflow.net/questions/38086/a-circle-packing-conjecture _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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