Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-24T19:18:15.645Z Has data issue: false hasContentIssue false

Note on Some Low-Order Perfect Squared Squares

Published online by Cambridge University Press:  20 November 2018

Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the Mathematical Games department of the Scientific American for November 1958 (12), William H. Tutte gave an entertaining account of the researches of himself and three colleagues (C. A. B. Smith, A. H. Stone, and R. L. Brooks) concerning "squaring the square." The problem is to subdivide a square into a finite number of non-overlapping smaller squares of which no two are the same size. At first suggested as impossible, a number of different solutions have been published. The first one, by Sprague in 1939 (9), showed a square divided into 55 smaller unlike squares.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Bouwkamp, C. J., On the dissection of rectangles into squares (Papers I, II, and III), Koninkl. Ned. Akad. Wettenschap., Proc. 49 (1946), 11761188; 50 (1947), 5871, 72-78.Google Scholar
2. Bouwkamp, C. J., On the construction of simple perfect squared squares, ibid., 50 (1947), 12961299.Google Scholar
3. Bouwkamp, C. J., Duijvestijn, A. J. W., and Medema, P., Catalogue of simple squared rectangles of order nine through fourteen and their elements (Eindhoven, 1960).Google Scholar
4. Bouwkamp, C. J., Duijvestijn, A. J. W., and Medema, P., Tables relating to simple squared rectangles of orders nine through fifteen (Eindhoven t 1960).Google Scholar
5. Brooks, R. L., Smith, C. A. B., Stone, A. H., and Tutte, W. T., The dissection of rectangles into squares, Duke Math. J., 7 (1940), 312340.Google Scholar
6. Brooks, R. L., Smith, C. A. B., Stone, A. H., and Tutte, W. T., A simple perfect square, Koninkl. Ned. Akad. Wettenschap., Proc, 50 (1947), 13001301.Google Scholar
7. Duijvestijn, A. J. W., Electronic computation of squared rectangles. Printed thesis, 1962, 92 pages (address of author: Philips Computing Centre, Eindhoven, Netherlands).Google Scholar
8. Goldberg, Michael, Review of (4). Math. Comput., 15 (1961), 315.Google Scholar
9. Sprague, R., Beispiel einer Zerlegung des Quadrats in lauter verschiedene Quadrate, Math. Z., 45 (1939), 607608.Google Scholar
10. Tutte, W. T., Question E 401 and solution, Amer. Math. Monthly, 47 (1940), 570572.Google Scholar
11. Tutte, W. T., Squaring the square, Can. J. Math., 2 (1950), 197209.Google Scholar
12. Tutte, W. T., Squaring the square. Scientific American (Nov. 1958), 136-142. Reprinted with Addendum and Bibliography in The 2nd Scientific American Book of Mathematical Puzzles and Diversions, by Martin Gardner (New York, 1961).Google Scholar
13. Willcocks, T. H., Fairy Chess Review, 7 (Aug./Oct. 1948).Google Scholar
14. Willcocks, T. H., A note on some perfect squared squares. Can. J. Math., 8 (1951), 304308.Google Scholar