*Packing the plane with discs*

### presented by Tom Kennedy

March 24, 2014

Suppose you have a bunch of pennies and want to arrange them
on your desk so that they do not overlap but cover as much of the desktop
as possible. Honeybees figured out the answer long ago, but a proof that
it is the optimal arrangement only came in 1890.
Now suppose you have two different sizes of coins and ask the
same question. The optimal arrangement depends on the relative sizes of
the coins, and lots of nice patterns emerge. For certain sizes
some especially nice packings known as "compact packing"
are possible. There are only finitely many, and we will attempt to
find as many as we can by drawing pictures, arranging discs, using
some simple planar geometry and whatever other tools come to mind.