You can for instance radially divide a disk of radius 2 into lots of approximately triangular wedges, divide each wedge into four roughly triangular pieces, and rearrange the pieces to form four approximate disks of radius 1.
an excellent observation. here's a small related puzzle. it's clear that you can cut a unit disk into two pieces that each contain a disk of radius 1/2. let phi = (sqrt5 - 1) / 2. let epsilon be a small positive number. how can you cut a unit disk into four pieces that can be rearranged in a non-overlapping fashion to form two regions that each contain a disk of radius phi - epsilon? (no piece covers more than one disk) no idea whether this is optimal, but it's the best i can do on an hour's notice and 6 hours sleep. erich