Lowest order squared rectangles and squares with the largest element not on the boundary
Authors:
A. J. W. Duijvestijn and P. Leeuw
Journal:
Math. Comp. 37 (1981), 223228
MSC:
Primary 05B45; Secondary 52A45
MathSciNet review:
616375
Fulltext PDF Free Access
Abstract 
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Abstract: The lowest order squared rectangles and squares with the largest element not on the boundary are presented.
 [1]
R.
L. Brooks, C.
A. B. Smith, A.
H. Stone, and W.
T. Tutte, The dissection of rectangles into squares, Duke
Math. J. 7 (1940), 312–340. MR 0003040
(2,153d)
 [2]
C.
J. Bouwkamp, On the dissection of rectangles into squares. I,
Nederl. Akad. Wetensch., Proc. 49 (1946), 1176–1188
= Indagationes Math. 8, 724–736 (1946). MR 0019310
(8,398e)
 [3]
P.
J. Federico, Squaring rectangles and squares, Graph theory and
related topics (Proc. Conf., Univ. Waterloo, Waterloo, Ont., 1977)
Academic Press, New YorkLondon, 1979, pp. 173–196. A historical
review with annotated bibliography. MR 538045
(80h:05019)
 [4]
W.
T. Tutte, A theory of 3connected graphs, Nederl. Akad.
Wetensch. Proc. Ser. A 64 = Indag. Math. 23 (1961),
441–455. MR 0140094
(25 #3517)
 [5]
Adrianus
Johannes Wilhelmus Duijvestijn, Electronic computation of squared
rectangles, Thesis, Technische Wetenschap aan de Technische Hogeschool
te Eindhoven, Eindhoven, 1962. MR 0144492
(26 #2036)
 [6]
A. J. W. Duijvestijn, Algorithmic Identification of Graphs and Determination of the Order of the Automorphism Group of a Graph, Memorandum 220, Twente University of Technology, Enschede, The Netherlands, 1978.
 [7]
A. J. W. Duijvestijn, Tables of Simple Squared Squares of Orders 13 Through 21 and Rectangles of Orders 17 Through 21, Twente University of Technology, Enschede, The Netherlands, 1979.
 [1]
 R. L. Brooks, C. A. B. Smith, A. H. Stone & W. T. Tutte, "The dissection of rectangles into squares," Duke Math. J., v. 7, 1940, pp. 312340. MR 0003040 (2:153d)
 [2]
 C. J. Bouwkamp, "On the dissection of rectangles into squares," Proc. Acad. Sci. Amsterdam, v. 49, 1946, pp. 11761188; v. 50, 1947, pp. 5878, 12961299 (= Indag. Math., v. 8, 1946, pp. 724736; v. 9, 1947, pp. 4363, 602625). MR 0019310 (8:398e)
 [3]
 P. J. Federico, "Squaring rectangles and squares," A historical review with annotated bibliography in Graph Theory and Related Topics (Bondy and Murphy, Eds.), Academic Press, New York, 1979, pp. 173196. MR 538045 (80h:05019)
 [4]
 W. T. Tutte, "A theory of 3connected graphs," Proc. Acad. Sci. Amsterdam, v. 64A, 1961 (= Indag. Math., v. 23, 1961, pp. 441455). MR 0140094 (25:3517)
 [5]
 A. J. W. Duijvestijn, "Electronic computation of squared rectangles," Philips Res. Rep., v. 17, 1962, pp. 523613. MR 0144492 (26:2036)
 [6]
 A. J. W. Duijvestijn, Algorithmic Identification of Graphs and Determination of the Order of the Automorphism Group of a Graph, Memorandum 220, Twente University of Technology, Enschede, The Netherlands, 1978.
 [7]
 A. J. W. Duijvestijn, Tables of Simple Squared Squares of Orders 13 Through 21 and Rectangles of Orders 17 Through 21, Twente University of Technology, Enschede, The Netherlands, 1979.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198106163750
PII:
S 00255718(1981)06163750
Keywords:
Squared rectangles,
dissection of rectangles,
tiling
Article copyright:
© Copyright 1981
American Mathematical Society
