Let delta(n) denote the self-circumference of a regular polygon with n sides. It will be shown that delta (n) is monotonically increasing from 6 to 2 pi if n is twice and odd number, and monotonically decreasing from 8 to 2 pi if n is twice an even number. Calculation of delta (n) for the case where n is odd as well as inequalities for self-circumference of some irregular polygons are given. Properties of the mixed area of a plane convex body and its polar dual are used to discuss the self-circumference of some convex curves. (kr)