[math-fun] ellipse packing

Puzzle: Choose some specific ellipse, say a=2 b=1. Find any packing that has a higher packing density than circles in the plane (the simple hex packing). I can beat the density of simple square packing of circles, by puting two 1x2 ellipses in a square, alternating horz and vertical in a checkerboard tiling, and then stretching the ellipses a smidgen. But this probably is still less than the circle-hex density. Rich