Dennis Clarke wrote in message <37C407D0.549A7778@interlog.com>...
>Kepler suggested this problem about
>400 years ago and suggested a solution that was correct, without the
benefit of
>x-ray crystalography or modern numerical methods.  His solution was based
on the
>simple observation that a man selling grape-fruit in the market will stack
in a
>close packed haxagonal plane and then add another layer on top of that one
>slightly shifted to allow the next layer to sit in the crevass between
three
>other touching grape-fruit on the lower layer.  Why?  Because it works.
The
>grape-fruit don't tumble over the edge and this seems to be a good
arrangement.
>There is plenty of lost volume in this packing but such is life.  If the
sphere
>radius is much smaller than the box dimensions then we have a solution.


This has been recently proven to be the correct solution.

Mark

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