A given rectangle can be entirely covered (i.e.
geometry/tiling/scaling
Problem
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?
Show solution
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.