rec.puzzles Archive

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.