I was fiddling with some numbers one afternoon and started with a string of square numbers 1,4,9,16,25,36,49,….pulling and pushing them around to see how they behaved. I decided to concatenate them 1,14,149,14916,1491625,149162536,….These quickly became too big for me to handle so I then cut them down to size by taking their digital roots 1,5,5,3,1,1,5,6,6,7,2,2,9,7,7,2,3,3,4,8,8,6,4,4,8,9,9... and realised that they form a beautiful repeating sequence. This work is inspired by the 27 terms which form the repeating sequence. There is light at the end of the tunnel.

24 Sums of Fibonacci

26" x 18", Acrylic on canvas, 2010

The digital roots of the Fibonacci Sequence repeats after every 24 terms and the repeating sequence is 1,1,2,3,5,8,4,3,7,1,8,9,8,8,7,6,4,1,5,6,2,8,1,9.

The 9 Digital Roots of Triangle Numbers

24" x 26", Acrylic on canvas, 2011

The Triangle Numbers 1,3,6,10,15,21,28.... have digital roots which are always 1,3,6 or 9. In fact, they form a repeating sequence of the following: 1,3,6,1,6,3,1,9,9...

Meditations on Symmetry

36" x 30", Acrylic on canvas, 2012

The Triangle Numbers 1,3,6,10,15,21,28....are an increasing sequence. Concatenated triangle numbers are 1,13,136,13610,1361015, 136101521,....another increasing sequence. The digital roots of the concatenated triangle numbers generate the repeating sequence 1,4,1,2,8,2,3,3,3,4,7,4,5,2,5,6,6,6,7,1,7,8,5,8,9,9,9,... This work is a meditation on that repeating sequence.

Pentagonal Numbers

20" x 18", Acrylic on canvas, 2011

Hexagonal Numbers

24" x 26", Acrylic on canvas, 2011

Heptagonal Numbers

34" x 24", Acrylic on canvas, 2011

Octagonal Numbers

20" x 18", Acrylic on canvas, 2011

The Octagonal numbers are 1,8,21,40,65,96,133,176,225,280,341,408,481,560,645,736,833,936,1045,1160,...

When the digital roots are taken, they form a repeating sequence1,8,3,4,2,6,7,5,9,...