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© Copyright 2003, Jim Loy
A perfect square dissection is when a square can be dissected into smaller squares, no two of which are equal. It was conjectured that this was impossible. But in 1939 a 55-square perfect square was shown by R. Sprague. The smallest solution is the 21-square dissection shown here, found in 1978 by A. J. W. Duijvestijn, with the help of a computer. It has a side of 112, and the size of each of the smaller squares is shown in the diagram above left.
Question: The second diagram appeared on the cover of Scientific American, in November 1958. It looks like a better solution. Is it? If not, what is wrong? See the answer here.
These diagrams was drawn with the program Cinderella.