From: dboll@pacifier.com (Dave Boll) Newsgroups: sci.math Subject: Packing circles and spheres. Date: 2 Sep 1996 03:43:57 GMT I thought I'd post a table of my current best packing results, since this is a topic that comes up occasionally on this newsgroups. Further discussion, and the programs used to generate the packings, can be found on my web site: http://www.pacifier.com/~dboll/ I have results for 4 cases: 1) Packing circles in squares. The unit square from (0,0) to (1,1) is used, the radius is given for the packing circle. 2) Packing circles in circles. The unit circle (radius of 1, centered at the origin) is used, the radius is given for packing circles. 3) Packing spheres in spheres. The unit sphere (radius of 1, centered at the origin) is used, the radius is given for packing spheres. 4) Points on the surface of a sphere. The unit sphere is used, and the minimum angle (in degrees) from the origin to any pair of points is given. Send email if you want to see any specific point list for a particular packing. I'm working on extending this table up to N=45, and solidfying my sphere-in-sphere results, since they aren't yet all that good. Packing results: Cir. in Squ Cir. in Cir. Sph in Sph Sphere surf 15 .127135 .220520 .316917 51.830 16 .125 .216182 .307899 50.959 17 .117087 .208272 .300890 47.690 18 .115472 .205601 .293341 46.426 19 .112239 .205601 .288100 45.922 20 .111379 .194088 .279672 44.154 21 .106592 .188218 .276479 42.985 22 .105516 .182291 .270770 41.980 23 .101707 .178442 .267833 40.776 24 .100123 .174819 .263250 39.179 25 .1 .172057 .259223 39.165 26 .096272 .169341 .257307 38.144 27 .095395 .167731 .253319 37.909 28 .093454 .165400 .249848 36.734 29 .091978 .161484 36.020 30 .091312 .160146 34.878 -- Dave Boll dboll@pacifier.com "Never use an outhouse toilet while holding your car keys in your mouth." Homepage: http://www.pacifier.com/~dboll/ Stop by for a visit! Lots of stuff on amateur Astronomy, recreational mathematics, etc.