plane cutting

Consider n intersecting circles. The maximal number of regions into which these divide the plane are N(n) = n^2 - n + 2, giving values for n = 1, 2, ... of 2, 4, 8, 14, 22, 32, 44, 58, ... (OEIS A014206).

arrangement | circle | circle division by lines | plane division by ellipses | plane division by lines | space division by spheres