February 09, 2004
Squaring the Square
Mathematician and quilter/knitter Pat Ashforth has created a textile piece based on a mathematical conundrum: "It depicts a square divided into the smallest known number of different squares which will fit together to make a square". The creation of the shape may be mathematical, but her color use is artistry.
I am no mathematician, so I looked up the history of this puzzle, and found a number of fascinating resources, which are all surprisingly attractive. Perhaps it is one of those 'harmonies of the spheres' events, where the mathematical proportions are inherently pleasing to nature and the human eye.
* Mathworld has a definition of this process that was the clearest to me - and related it to quilting: "A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which the squares need not be different sizes are called Mrs. Perkins's quilts." (note: this link has 21 types of Mrs. Perkins Quilts).
Some historic tidbits: "In 1936, four students at Trinity College considered the problem of cutting up a rectangle into squares of unequal size (no two alike)."
The ultimate site is devoted solely to squared squares and rectangles: www.squaring.net "This website has been designed to bring together for reference and display, many of the tilings of squared squares and squared rectangles which have been discovered over the last hundred years, up until recent times." If you browse the folders on the left, there are links to interactive square drawing web applets. Choosing 'image8' will generate op art (psychedelic?) results! see below
image(above right): Square Deal by Pat Ashforth
image (left): perfect squared square; order 21;1 generated at www.squaring.net
