Suman Vaze

Artist, Maths teacher
King George V School
Hong Kong

In these paintings I explored and visually enumerated all the possible ways of arranging non-overlapping circles. I found that the maximum number of possible arrangements of N such circles formed the sequence 1,2,4,9, 20, 48,115,….Checking for this sequence I found that it was the number of unlabeled rooted trees with n nodes (A000081 OEIS).

This is the general method of my artistic practice where I meander through my own experiments in visual thinking and stumble upon hidden mathematics.

Families V - Lily pads
75 x 60 cm
acrylic on canvas

n non-overlapping, entirely nested or dis-joint circles can be drawn in a maximum of 1, 2, 4, 9, 20, 48, 115,…ways, where nϵN . This painting shows all the 20 possible arrangements with 5 circles.

Blue Moon
75 x 75 cm
acrylic and oil stick on canvas

This painting seeks to visually describe all the 16 possible ways in which 1, 2, 3 or 4 circles can be drawn so that they are either entirely nested or dis-joint but do not overlap other circles.