Improved Dense Packings of Congruent Squares in a Square

Abstract

Let s_n be the side of the smallest square into which it is possible to pack n congruent squares. In this paper we link s_n to the supremum of the maximal inflation Ω (C) of admissible configurations C. The computation and the properties of Ω in a bounded domain. We improve the best known packings of n equal squares for n=11, 29 and 37, and give an alternative optimal packing of 18 squares.

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1. LMPA, Universitédu Littoral, 50 rue F. Buisson, BP699, 62228 Calais Cedex, France

   Thierry Gensane & Philippe Ryckelynck

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1. Thierry Gensane
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2. Philippe Ryckelynck
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Correspondence to Thierry Gensane or Philippe Ryckelynck.

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Gensane, T., Ryckelynck, P. Improved Dense Packings of Congruent Squares in a Square. Discrete Comput Geom 34, 97–109 (2005). https://doi.org/10.1007/s00454-004-1129-z

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• Received: 08 April 2004

• Revised: 19 May 2004

• Published: 20 October 2004

• Issue date: July 2005

• DOI: https://doi.org/10.1007/s00454-004-1129-z

Keywords

• Computational Mathematic
• Bounded Domain
• Dense Packing
• Optimal Packing
• Maximal Inflation