plane cutting

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, ... (OEIS A051890).

arrangement | circle division by lines | ellipse | plane division by circles | plane division by lines