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Plane Division

Consider $n$ intersecting Circles and Ellipses. The maximal number of regions in which these divide the Plane are

$\displaystyle N_{\rm circle}$ $\textstyle =$ $\displaystyle n^2-n+2$  
$\displaystyle N_{\rm ellipse}$ $\textstyle =$ $\displaystyle 2n^2-2n+2.$  

See also Arrangement, Circle, Cutting, Ellipse, Space Division




© 1996-9 Eric W. Weisstein
1999-05-25