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Last updated: Mon Dec 1 2008

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Discrete Mathematics > Division Problems >

Plane Division by Ellipses
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PlaneDivisionbyEllipses

Consider n intersecting ellipses. The maximal number of regions into which these divide the plane are

N(n)=2n^2-2n+2=2(n^2-n+1),

giving values for n=1, 2, ... of 2, 6, 14, 26, 42, 62, 86, 114, ... (Sloane's A051890).

SEE ALSO: Arrangement, Circle Division by Lines, Ellipse, Plane Division by Circles, Plane Division by Lines

REFERENCES:

Sloane, N. J. A. Sequence A051890 in "The On-Line Encyclopedia of Integer Sequences."

Problem Q607. Parabola 20, 27, 1984.




CITE THIS AS:

Weisstein, Eric W. "Plane Division by Ellipses." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PlaneDivisionbyEllipses.html

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