Perfect Square Packings

✍ Scribed by Adam Chalcraft

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 185 KB
• Volume: 92
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.2000.3058

✦ Synopsis

An interesting problem is to determine whether all the squares of side n &1 can be packed into a rectangle of the appropriate area. Such a packing (into a rectangle of the right area) is called perfect. In this paper, we define an algorithm based on an algorithm by Paulhus and use it to show that there is a perfect packing of the squares of side n &3Â5 into a square. The technique can be used to prove that there is a perfect packing of the squares of side n &t into a square, where 1Â2<t 3Â5, provided a certain algorithm succeeds for that value of t. It has succeeded for every such value of t that the author has tried. We also show that there is a perfect packing for all t in the range 0.5964 t 0.6.