Perfect square packings

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(-3/5) into a square. The technique can be used to prove that there is a perfect packing of the squares of side n(-1) into a square, where 1/2 < t <less than or equal to> 3/5, 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 less than or equal to t less than or equal to 0.6. (C) 2000 Academic Press.