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
IN PRIVATE COLLECTION
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
Commissioned and bought for display on the wall in the client reception room in barristers’ chambers in Lincoln’s Inn, London.
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