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.
, 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
![n+[(n-1)+f(n-2)]](/images/equations/CircleDivisionbyLines/Inline16.svg)
,
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.
