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Packing squares into rectangles

Published online by Cambridge University Press:  23 January 2015

Richard Ellard  and
Des MacHale
Richard Ellard
Affiliation:
School of Mathematical Sciences, University College Cork, Ireland, e-mails:richardellard@gmail.com; d.machale@ucc.ie
Des MacHale
Affiliation:
School of Mathematical Sciences, University College Cork, Ireland, e-mails:richardellard@gmail.com; d.machale@ucc.ie
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Extract

In this paper, we collect some results on a problem which has been considered by many authors over the years, including Ed Pegg Jr., R. M. Kurchan, William Rex Marshall, David Neary, Richard Korf and Eric Huang. The results have been rediscovered many times by many people, including the present authors, but very little has been published, except in a little known journal which no longer appears. Some of the cases have been solved by hand while others have been covered by Korf [1, 2], using a computer. We see our main role as that of collectors of information and presenters of results, in the hope that others will be inspired to study what is an exciting and very interesting area of combinatoric geometry; we believe, however, that some of our observations, variations and upper bounds are new.

Type
Articles
Information
The Mathematical Gazette , Volume 96 , Issue 535 , March 2012 , pp. 1 - 18
Copyright
Copyright © The Mathematical Association 2012

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References

1. Anglin, W. S., The square pyramid puzzle, The American Mathematical Monthly 97 (February 1990) pp. 120–124.Google Scholar
2. Huang, Eric and Korf, Richard E., New improvements in optimal rectangle packing, Proceedings of the 21st international joint conference on artifical intelligence, Pasadena, California, USA (2009) pp. 511–516.Google Scholar
3. Korf, Richard E.. Optimal rectangle packing: new results, Proceedings of the International Conference on Automated Planning and Scheduling (ICAPS04), Whistler, British Columbia (June 2004) pp. 142–149.Google Scholar