Bogus geometry problem ```Name: murphy Status: N/A Age: N/A Location: N/A Country: N/A Date: Around 1995 ``` Question: It is possible to divide up a square into four pieces and rearrange them to give the square a greater area. Of course, you laugh, but it works, like it or not. A square that 8" on each side has an area of 64 square inches. Now cut down three inches from the top straight across. Cut this top rectangle (8x3") diagonally, so two triangles a are made whose two straight bases are 3 and 8 inches each. They share a common diagonal. Still having the overall square form, cut 3 inches from the bottom left hand corner, to exactly three inches in from the left right hand side, at three inches down from the right hand corner at the top. (Note: The cut from the bottom left is on the bottom of the square, not the side of it.) If you do this right you get two triangles and two quadrilaterals. By arranging these so the three inch face of the quads, matches the three inch base of the triangles, you get a rectangle with an area of 65 square inches. Yes, it is true! So much for law of conservation of energy and matter! An extra cubic inch from nowhere! Enjoy this one, fellows. It can make you rich at the local hangout! Replies: BOGUS! This is from a recent issue of the International Journal of Theoret- ical Physics and has since been shown to be bogus. The trick is in the rearrangement there are very small gaps. hawleyActually though, the axioms often used in mathematics allow something essentially equivalent to this to be done, if you allow people to make cuts of somewhat infinite complexity. There was a cute article describing this in the "recreational mathematics" section of Scientific American some years back. Sorry I do not have the exact reference. Of course, it is not a very practical approach (particularly since materials are not infinitely divisi- ble - there are atoms down there after all) so this is really just something for mathematicians to have fun with and make them worry about the consisten- cy of some of their axioms. asmith Click here to return to the Mathematics Archives

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