Original Art by Ian P. Hudson — Squares

Squared Squares

These paintings are inspired by the minimal* solution by A.J.W.Duijvestijn (in 1978) of the “squared square” or perfect square dissection problem — dissection of a square into smaller squares all of different sizes, and with no subset of them forming a rectangle.

My own mathematical contribution was to find a colour scheme such that the 21 squares form six sets each of a single colour, the sets comprising respectively 1, 2, 3, 4, 5, ∓ 6 squares, such that no squares of the same colour have a common border. In my chosen solution, the smallest square is the sole member of its set**.

* “Minimal” means that there is no solution with fewer than 21.

** I invite mathematicians to try to prove or disprove that this is true of every such colouring solution for this 21-square dissection!

21 Squares Blues painting thumbnail 21 Squares Blues (2004)
606 × 606 mm
Acrylic on board
£250.00
42 Summer thumbnail42 Winter thumbnail Diptych: 42 Squares Summer and Winter (2004)
Two pieces, each 606 × 606 mm
Acrylic on board
IN PRIVATE COLLECTION
Diptych Warm thumbnailDiptych Cool thumbnail Diptych: Warm and Cool (2004)
Two pieces, each 404 × 404 mm
Acrylic on board
IN PRIVATE COLLECTION
21 Squares Blues painting thumbnail 4x21 Squares The Four Seasons (2004)
606 × 606 mm
Acrylic on board
£380.00
21 Squares Nested painting thumbnail 21 Squares Nested (2003)
1210 × 1210 mm
Emulsion on board
£500.00