Take two points on a circle,

and draw a line straight through.

The space that was encircled

is divided into two.

To these points add a third one,

which gives us two more chords.

The space through which these lines run

has been fissured into four.

Continue with a fourth point,

and three more lines drawn straight.

The new number of disjoint

regions sums, in all, to eight.

A fifth point and its four lines

support this pattern gleaned.

Counting sections, one divines

that there are now sixteen.

This pattern here of doubling

does seems a sturdy one.

But one more step is troubling

as the sixth gives thirty one.