THE SHAPE OF A PLANE SECTION OF MAXIMUM MOMENT OF INERTIA

The paper solves the Following geometrical problem: of all plane convex domains of given area find the one with the largest value of the least second moment of area (moment of inertia) about any line through the centroid of the domain. It is shown that the domain must have the same moment of inertia about every line through its centroid and that among a family of convex domains the equilateral triangle solves the geometrical problem.