Plane division by ellipses is the partition of the plane into regions by an arrangement of 
ellipses, where 
is a nonnegative integer.
For 
,
the maximal number of regions is
giving values for 
, 2, ... of 2, 6, 14, 26, 42, 62, 86, 114, ... (OEIS A051890).
The maximum is attained when each pair of ellipses intersects in four distinct points
and no three ellipses pass through the same point.
For 
,
the 
th
ellipse then adds 
regions. With no ellipses,
.
See also
Arrangement,
Circle Division by Lines,
Ellipse,
Plane
Division by Circles,
Plane Division by Lines
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References
--. Problem Q607. Parabola 20, 27, 1984.Sloane, N. J. A. Sequence A051890 in "The
On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Plane Division by Ellipses
Cite this as:
Weisstein, Eric W. "Plane Division by Ellipses."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PlaneDivisionbyEllipses.html
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