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?

Sure.

You can chop the circle into infinitesmal dust (taking care to stay some distance epsilon from the centre) then glue the dust back into two semicircles; your favourite fractal or any other shape you fancy.

Perhaps the query should limit solutions to procedures involving some small number of cuts. I don't mean to be provocative, but right now I'm really left guessing what is wanted.. 

Posted by FrankM on 2008-01-18 01:16:51