🚀 go-pugleaf

In article <1993Jan26.235433.18005@cs.ucla.edu>
byron elbows writes:

> I need help on a sphere packing question.  Suppose you have a white ping
> pong ball, and 13 red ones, all the same size.  Can you glue all of the red
> ping pong balls to the white one?  In other words, is it possible to place
> 13 unit spheres around one unit sphere, so that each of the 13 is touching
> the central sphere, and none of the 13 intersect each other?
> 
> It is a simple matter to do it with 12.  Simply place the spheres at the
> corners of an icosahedron centered at the center of the white ping pong ball.
> It turns out this leaves some extra room for spheres to be moved around, but
> is it possible to move them around so that another sphere can be squashed
> in there?

You're asking a question about the 'kissing number'; that is, the
greatest number of objects that can be touching another object of the
same size.  For two dimensions (ie. circles), the kissing number is 6,
and for three dimensions (spheres -- the question you ask), it's been
proven that the kissing number is 12.  Therefore, there is no way to
move those twelve spheres to make a 13th one touch the center sphere. 
Sometime within the last year (sorry I don't have the exact date!)
Scientific American ran a piece about the kissing number in its math
column.


--Ted Schuerzinger
email: .zed@Dartmouth.EDU
"I should have realized it would be bad vodka when all the label said
was 'Russian Vodka'."