This article is from the Puzzles FAQ, by Chris Cole email@example.com and Matthew Daly firstname.lastname@example.org with numerous contributions by others.
A given rectangle can be entirely covered (i.e. concealed) by an
appropriate arrangement of 25 disks of unit radius.
Can the same rectangle be covered by 100 disks of 1/2 unit radius?
Yes. The same configuration of circles, when every distance is reduced
by half (including the diameters), will cover a similar rectangle whose
sides are one half of the original one. The original rectangle is the
union of four such rectangles.