If anyone finds improved packings of unit circles in ellipses, I would greatly appreciate their sending me a copy of whatever they send Erich. Furthermore, for anyone wanting to work on that packing problem, I can easily provide, on request, details of all the packings in the form of a Mathematica (v. 5.2) notebook. David W. Cantrell ----- Original Message ----- From: "James Buddenhagen" <jbuddenh@gmail.com> To: "math-fun" <math-fun@mailman.xmission.com> Sent: Sunday, October 07, 2007 14:51 Subject: [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
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