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A014530
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List of sizes of squares occurring in lowest order example of a perfect squared square.
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8
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2, 4, 6, 7, 8, 9, 11, 15, 16, 17, 18, 19, 24, 25, 27, 29, 33, 35, 37, 42, 50
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listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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A squared rectangle (which may be a square) is a rectangle dissected into a finite number, two or more, of squares. If no two of these squares have the same size the squared rectangle is perfect. A squared rectangle is simple if it does not contain a smaller squared rectangle, and compound if it does. The order of a squared rectangle is the number of constituent squares. Duijvestijn's perfect square of lowest order (21) is simple. The lowest order of a compound perfect square is 24. [Geoffrey H. Morley, Oct 17 2012]
See the MathWorld link for an explanation of Bouwkamp code. The Bouwkamp code for the squaring is (50,35,27)(8,19)(15,17,11)(6,24)(29,25,9,2)(7,18)(16)(42)(4,37)(33). [Geoffrey H. Morley, Oct 18 2012]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences. Academic Press, San Diego, 1995, Fig. M4482.
I. Stewart, Squaring the Square, Scientific Amer., 277, July 1997, pp. 94-96.
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LINKS
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EXAMPLE
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Terms | 2 4 6 7 8 9 11 15 16 17 18 19 24 25 27 29 33 35 37 42 50
-------------------------------------------------------------------------
| <-- sort selected groups
-------------------------------------------------------------------------
(50,35,27) | . . . . . . . . . . . . . . 27 . . 35 . . 50
(8,19) | . . . . 8 . . . . . . 19 . . . . . .
(15,17,11) | . . . . . 11 15 . 17 . . . . . . .
(6,24) | . . 6 . . . . 24 . . . . .
(29,25,9,2)| 2 . . 9 . . 25 29 . . .
(7,18) | . 7 . 18 . . .
(16) | . 16 . . .
(42) | . . . 42
(4,37) | 4 . 37
(33) | 33
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Groups of terms selected and sorted for the Bouwkamp piling
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The Bouwkamp code says how to pile up the squares in order to tile the square with side length 50 + 35 + 27 = 112. The procedure is beautifully animated in World of Mathematics (see link section).
(End)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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