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%I #31 Jun 21 2021 03:07:34
%S 2,4,6,7,8,9,11,15,16,17,18,19,24,25,27,29,33,35,37,42,50
%N List of sizes of squares occurring in lowest order example of a perfect squared square.
%C 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]
%C 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]
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences. Academic Press, San Diego, 1995, Fig. M4482.
%D I. Stewart, Squaring the Square, Scientific Amer., 277, July 1997, pp. 94-96.
%H <a href="https://www.srcf.ucam.org/tms/about-the-tms/the-squared-square/">The Trinity Mathematical Society logo</a>
%H C. J. Bouwkamp and A. J. W. Duijvestijn, <a href="http://alexandria.tue.nl/repository/books/391207.pdf">Catalogue of Simple Perfect Squared Squares of orders 21 through 25</a>, EUT Report 92-WSK-03, Eindhoven University of Technology, Eindhoven, The Netherlands, November 1992.
%H C. J. Bouwkamp and A. J. W. Duijvestijn, <a href="http://alexandria.tue.nl/repository/books/430534.pdf">Album of Simple Perfect Squared Squares of order 26</a>, EUT Report 94-WSK-02, Eindhoven University of Technology, Eindhoven, The Netherlands, December 1994.
%H A. J. W. Duijvestijn, <a href="http://doc.utwente.nl/68433/1/Duijvestijn78simple.pdf">Simple perfect square of lowest order</a>, J. Combin. Theory Ser. B 25 (1978), 240-243.
%H N. D. Kazarinoff and R. Weitzenkamp, <a href="http://deepblue.lib.umich.edu/bitstream/2027.42/33904/1/0000169.pdf">On the existence of compound perfect squared squares of small order</a>, J. Combin. Theory Ser. B 14 (1973).163-179. [A compound perfect squared square must contain at least 22 subsquares.]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectSquareDissection.html">Perfect Square Dissection</a>
%H <a href="/index/Sq#squared_squares">Index entries for squared squares</a>
%e Example from _Rainer Rosenthal_, Mar 25 2021: (Start)
%e .
%e Terms | 2 4 6 7 8 9 11 15 16 17 18 19 24 25 27 29 33 35 37 42 50
%e -------------------------------------------------------------------------
%e | <-- sort selected groups
%e -------------------------------------------------------------------------
%e (50,35,27) | . . . . . . . . . . . . . . 27 . . 35 . . 50
%e (8,19) | . . . . 8 . . . . . . 19 . . . . . .
%e (15,17,11) | . . . . . 11 15 . 17 . . . . . . .
%e (6,24) | . . 6 . . . . 24 . . . . .
%e (29,25,9,2)| 2 . . 9 . . 25 29 . . .
%e (7,18) | . 7 . 18 . . .
%e (16) | . 16 . . .
%e (42) | . . . 42
%e (4,37) | 4 . 37
%e (33) | 33
%e _________________________________________________________________________
%e Groups of terms selected and sorted for the Bouwkamp piling
%e .
%e 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).
%e (End)
%Y Cf. A002839, A002962, A002881, A342558 (related by the analogy between square tilings and resistor networks).
%K nonn,fini,full
%O 1,1
%A _N. J. A. Sloane_
%E 'Simple' removed from definition by _Geoffrey H. Morley_, Oct 17 2012
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