Arrangements of Nested Circles

Regular price $30.00

This 18x24" poster shows all of the ways that N circles can be nested (without intersecting one another) for N = 1 to 7.

Each arrangement is labeled in parenthetical notation with the letter `o` representing leaf nodes and pairs of parentheses representing circles that contain other circles. 

Each arrangement is distinct - no two can be reached from one another by moving circles around without passing through an intersection. For example, (o)o is considered the same as o(o), so only one of these is shown.

The number of arrangements for a given N is the OEIS sequence A000081 with values 1, 2, 4, 9, 20, 48, 115... This sequence also has other derivations and interpretations.

I created this design with custom Python code. I was inspired by a more difficult problem which allows circles to overlap, as discussed in this excellent Numberphile video.