Plane division by lines is the partition of a plane into regions by an arrangement of 
lines, where 
is a nonnegative integer.
The maximal number of regions is
 |
which, for 
,
2, ... gives 2, 4, 7, 11, 16, 22, ... (OEIS A000124),
the same maximal number of regions into which a circle
or square can be divided by 
lines. The maximum for the plane
is attained when no two lines are parallel
and no three pass through the same point. Each additional
line then adds 
regions, starting from 
.
