A circular disk can be cut into two semicircular pieces easily by cutting along a diameter.

Can the disk be cut into pieces which can be arranged into two semicircles, with none of the cuts passing through the center?

... cut any convenient shape, centered on the center of the circle, say a square.  Then cut what's left of the circle into two pieces as if the cuts were going to go to the center that's no longer there.  Then cut the same shape you originally cut from around the center from each of the two larger pieces (near semicircles), and cut one of those two new plugs in half. Place one of these halves into each of the semi-holes along the original diameter, along the flat sides of the semicircles, and use the complete squares to plug the complete holes you made in the two semicircles.

Posted by Charlie on 2007-04-27 14:33:07