A military bride travelling in Afghanistan is surprised when a mystic is able to cut up a chess board ("with three snips of my scissors") and put it back together so that the number of squares has increased from 64 to 65. An illustration of the cuts used appears in the text and seems at first to lead to the contradictory conclusion that 64=65:
Of course, it is not actually possible to change the area of a board from 64 square inches to 65 square inches with three cuts and some rearrangement. The explanation is that there are small deviations in the rearrangement that are too subtle for us to see with the naked eye. (In other words, the right triangle you see in the second figure is not actually a right triangle!) For a similar "paradox" and an explanation, see MathWorld's description of the Triangle Dissection Paradox.
(Appeared as Harper's New Monthly Magazine, 10 (1885), 359—73.) |