'Special' Perfect Squared Squares

'Special' Perfect Squared Squares are Perfect Squared Squares, which have some features or property which makes them 'special'.

DEFINITIONS: A squared rectangle is a rectangle dissected into a finite number, two or more, of squares, called the elements of the dissection. If no two of these squares have the same size the squared rectangle is called perfect, otherwise it is imperfect. The order of a squared rectangle is the number of constituent squares. The case in which the squared rectangle is itself a square is called a squared square. The dissection is simple if it contains no smaller squared rectangle, otherwise it is compound. Simple Perfect Squared Squares are SPSSs, Compound Perfect Squared Squares are CPSSs, a Perfect Squared Square can be an SPSS or a CPSS and is a PSS. Simple Imperfect Squared Squares are SISSs, Simple Perfect Squared Rectangles are SPSRs, and so on ...

Among the characteristics which mark PSSs as being 'special' are items in the following list;


  1. 'O Rozkladach Prostokatow Na Kwadraty' (On the Dissection of a Rectangle into Squares) by Zbigniew Moroń, Prezeglad Mat. Fiz. 3 152-153 (1925)
  2. R.L. Brooks, C.A.B. Smith, A.H. Stone and W. T. Tutte. 'The Dissection of Rectangles into Squares'. Duke Math. J. 7 (1940) 312–340.
  3. E401 A. H. Stone, Michael Goldberg and W. T. Tutte, The American Mathematical Monthly Vol. 47, No. 8 (Oct., 1940), pp. 570-572
  4. JASPER DALE SKINNER II, 'Uniquely Squared Squares of a Common Reduced Side and Order', JOURNAL OF COMBINATORIAL THEORY, Series B 54, 155-156 (1992)
  5. T. H. WILLCOCKS, A note on some perfect squared squares, Canad. J. Math. 3 (1951),304-308.
  6. W. T. Tutte, Squaring the square, Canad. J. Math. 2 (1950),197-209.
  7. W. T. Tutte, The Quest of the Perfect Square, The American Mathematical Monthly, Vol. 72, No. 2, Part 2: Computers and Computing (Feb., 1965), pp. 29-35
  8. A.J.W. Duijvestijn and P.Leeuw, Lowest Order Squared Rectangles and Squares With the Largest Element Not on the Boundary, Mathematics of Computation, Vol. 37, No. 155 (Jul., 1981), pp. 223-228