Square of Squared Squares
Materials and Methods: Needlepointed with silk & ivory yarn on 18 stitches/inch canvas
Designer: Danny Otero
Artists: Danny and Debbie Otero
Year: 2010--2011
A perfectly squared rectangle is a rectangle tiled with squares all of which have different side lengths. Perfectly squared squares have a very appealing artistic effect, as the tiles and the figure being tiled are the same shape. A simple perfect squared square (SPSS) contains no smaller rectangular subsection of tiles.
The first example of an SPSS, of order 38 (using 38 square tiles), was discovered by Brooks in 1939. In 1962 A.J.W. Duijvestijn was able to prove that no SPSS existed of order less than 20. In 1978 Duijvestijn found a SPSS of order 21 and by 1992 he had found all the lowest-ordered SPSS, of order less than 26. It wasn't until 1999 that I. Gambini confirmed that three SPSS Duijvestijn catalogued, two of order 22 and one of order 23, were of minimal size; each of these was 110 units to a side, while the minimal SPSS of order 21 was 112 units to a side.
The four needlepoints here represent the smallest SPSS. Each is displayed in a different color family of yarns made of silk and wool: the SPSS of order 21 is shown in 21 different shades of red and orange; the two of order 22 are in yellows and browns and in greens and grays; and the one of order 23 is in blues and purples.