Plane Division by Lines


The maximal number of regions into which n lines divide a plane are


which, for n=1, 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 n lines.

See also

Arrangement, Circle Division by Lines, Line, Plane Division by Circles, Plane Division by Ellipses, Square Division by Lines

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Sloane, N. J. A. Sequence A000124/M1041 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Plane Division by Lines

Cite this as:

Weisstein, Eric W. "Plane Division by Lines." From MathWorld--A Wolfram Web Resource.

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