Circle division by lines, also called the circle cutting or pancake cutting problem, asks for the maximum number of regions into which distinct straight lines passing through
the interior of a closed disk can divide it, where
is a nonnegative integer. The minimum
number is , and every number of regions between the minimum
and maximum is attainable. For a maximum
arrangement, the th
cut creates
new regions. With , the first values and recurrence for are
(1)
(2)
(3)
For , this gives
(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.
The pizza theorem concerns the areas of alternating slices when the cuts meet at equal angles
at a common interior point.
of regions into which 
distinct straight lines passing through
the interior of a closed disk can divide it, where
is a nonnegative integer. The minimum
number is 
, and every number of regions between the minimum
and maximum is attainable. For a maximum
arrangement, the 
th
cut creates 
new regions. With 
, the first values and recurrence for 
are
, this gives
![n+[(n-1)+f(n-2)]](/images/equations/CircleDivisionbyLines/Inline21.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.
