Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 36 (1995), No. 1

On the Lower Bound of Packing Density for Convex Bodies in the Plane

Kevin R. Doheny

G. Kuperberg and W. Kuperberg [12] proved that every convex plane 
body $K$ admits a packing in the plane with congruent copies of $K$ 
with density 
at least $\sqrt{3}/2$. The author improves on this result by showing 
that there is a number $r_0 > \sqrt{3}/2$ so that 
if $K$ is a convex plane body, then $K$ admits a packing in the plane by 
congruent copies of $K$ with density at least $r_0$. 
The number $r_0$ is not shown explicitly.