Take a square and cut it as you wish into a finite number of pieces. Rearrange the pieces without rotating or flipping any of them to form an new square that is rotated 45-degrees compared to the original.

(In reply to Oops! by SteveH)

I downloaded the "squares" separately as .jpgs and printed them separately after blowing them up by a factor of 2. The result was that they each had the same area, namely 16 sq. in., and the pieces were the same size in each, of course. However, the second "square" had dimensions 3sqrt(2)~=4.24 by (8/3)sqrt(2)~=3.77.

I don't see where your 1.12 comes from, or how it is relevant. The ratio of the side lengths of the new "square" is 1.125, but it is dimensionless.

Edited on October 21, 2004, 6:05 am

Posted by Richard on 2004-10-21 03:34:38