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.

Draw a square with vertical sides. Mark an X in the square, with the lines of the X reaching corner to corner. Cut along these lines, giving you 4 equal sized triangles. From the top triangle clockwise, label the triangles 1-4.

Make 1 the bottom of the new square, move 2 to the left of 1 (making a right angle where the long sides touch). Place 3 on the top, and 4 on the right.

You now have a square at 45 degress tilt, albeit twice the size of the original.

Does that make any sense? And sorry if someone else has written this solution; I didn't read all the posted comments!

Posted by geegee on 2004-10-20 16:44:45