ABSTRACT
Let C be a disk, i.e., a convex, compact set on the Euclidean plane with interior points. Let H={C 1,…,C i ,…} be a (finite or infinite) sequence of disks. We say that H permits a translation covering of C if there exist translations т i such that
Moser and Moon [11] showed that if Q is the unit square and H is a
family of squares of sizes x 1,x 2,…with total area and with sides parallel to the sides of Q, then H permits a translation covering of Q. This is the best possible bound as one can see from the case when x 1=x 2=x 3=1−ε, x 4=…=0.
