A dissection fallacy is an apparent paradox arising when two plane figures with different areas seem to be composed by the same finite set of parts. In order to produce this illusion, the pieces have to be cut and reassembled so skillfully, that the missing or exceeding area is hidden by tiny, negligible imperfections of shape. A strikingly simple and enlightening example can be constructed by dissecting an 8×8 checkerboard in four pieces as depicted. The middle and right figures then seem to demonstrate that the same pieces can give rise to two different polygons having area 5×13 = 65 and 2(5×6) + 3 = 63, respectively. This would imply that 63 = 64 = 65.

Curry triangle | dissection | dissection puzzles | fallacy | tangram paradox | triangle dissection paradox