Determining the maximum number of pieces in which it is possible to divide a circle for a given number of cuts is called the circle cutting or pancake cutting problem.
The minimum number is always , where is the number of cuts, and it is always possible to obtain
any number of pieces between the minimum and maximum. The first cut creates 2 regions,
and the th
cut creates
new regions, so

(1)

(2)

(3)

Therefore,

(4)

(5)

(6)

(7)

(8)

Evaluating for ,
2, ... gives 2, 4, 7, 11, 16, 22, ... (OEIS A000124).
This is equivalent to the maximal number of regions into which a plane
can be cut by
lines.