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A Class of Self-Dual Maps

Published online by Cambridge University Press:  20 November 2018

C. A. B. Smith  and
W. T. Tutte
C. A. B. Smith
Affiliation:
University College, LondonUniversity of Toronto
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1. Introduction. A dissection of a rectangle R into a finite number n of non-overlapping squares is called a squaring of R of order n. The n squares are called the elements of the dissection. If there is more than one element and the elements are all unequal the squaring is called perfect and R is a perfect rectangle. (We use R to denote both a rectangle and a particular squaring of it). If a squared (perfect) rectangle is a square we call it a squared (perfect) square.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 2 , 1950 , pp. 179 - 196
Copyright
Copyright © Canadian Mathematical Society 1950

References

[1] Brooks, R. L., Smith, C. A. B., Stone, A. H. and Tutte, W. T., “The Dissection of Rectangles into squares,” Duke Math. J . , vol. 7 (1940), 312–340.Google Scholar
[2] Jeans, J. H., The Mathematical Theory of Electricity and Magnetism (Cambridge, 1908).Google Scholar
[3] Aitken, A. C., Determinants and Matrices (Edinburgh, 1939).Google Scholar
[4] Kerékjártό, B. v., “Über die periodischen Transformationen der Kreisscheibe und der Kugelfiache,” Math. Ann., vol. 80 (1919),36–38.Google Scholar
[5] Veblen, O., Analysis Situs (Amer. Math. Soc. Colloquium Publications, 2nd ed. (1913)).Google Scholar
[6] Bouwkamp, C. J., On the Dissection of Rectangles into Squares, Papers I and II. (Koninklijke Nederlandsche Akademie van Wetenschappent Proc, vol. 49 (1946), 1176-1188, and vol. 50 (1947), 58–71).Google Scholar