The maximal number of regions into which 
lines divide a plane are
 |
which, for 
,
2, ... gives 2, 4, 7, 11, 16, 22, ... (OEIS A000124),
the same maximal number of regions into which a circle, square, etc. can be divided
by 
lines.
Plane Division by Lines
See also
Arrangement, Circle Division by Lines, Line, Plane Division by Circles, Plane Division by Ellipses, Square Division by LinesExplore with Wolfram|Alpha
References
Sloane, N. J. A. Sequence A000124/M1041 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Plane Division by LinesCite this as:
Weisstein, Eric W. "Plane Division by Lines." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlaneDivisionbyLines.html