On Thursday 08 December 2005 03:34, dasimov@earthlink.net wrote:
The recent discussion re packing of various equiareal ellipses reminds me of a question discussed in this venue some years ago -- but I don't recall the upshot: Which bounded planar convex shape W, packed as well as possible, has the lowest density?
http://www.home.unix-ag.org/scholl/octagon.html has a proposal. The MathWorld article on "circle packing" includes this paragraph: | Surprisingly, the circular disk is not the least economical region | for packing the plane. The "worst" packing shape is not known, | but among centrally symmetric plane regions, the conjectured candidate | is the so-called smoothed octagon. which refers to the same shape as the page above. -- g