Almost-tiling the plane by ellipses
  For any delta > 1 we construct a periodic and locally finite packing of the plane with ellipses whose delta-enlargement covers the whole plane. This answers a question of Imre B\'ar\'any. On the other hand, we show that if C is a packing in the plane with circular discs of radius at most 1, then its 1.00001-enlargement covers no square with side length 4. 
Krystyna Kuperberg, W{\l}odzimierz Kuperberg, Ji\v{r}\'i Matou\v{s}ek,   Pavel Valtr