On Fri, 10 Nov 2006, David W. Cantrell wrote:
Anyway, if anyone can improve some of the packings shown on Erich's page, he and I would certainly be interested.
I tweaked the program to recursively search for the minimum r that supports a number of squares (in my parallel-row form): http://lunkwill.org/src/square-in-circle/ Graphics in: http://lunkwill.org/src/square-in-circle/svg-minimum-r/ (David's quadratic approximation comes in handy there - thanks!) Interestingly, for n=5..35, my algorithm is usually within 5% of the tilted solutions. n=35 is actually one of the biggest differences: Eppstein got 3.640 vs my 3.760. n=11 seems to almost not exist at all in row-parallel form: my algorithm stops trying at a delta r of 1e-7, and for n=11 gave up at r=2.236068, where it actually fit 12 squares.