Moment-of-inertia triangle inequalities
= Moment-of-inertia triangle inequalities
{title2=$I_x+I_y\ge I_z$}
For three mutually perpendicular axes through one point of a nonnegative <mass distribution>, $I_x+I_y-I_z=2\int z^2\,dm\ge0$, with cyclic counterparts. Equality holds precisely when the <mass distribution> is supported in the plane $z=0$, giving the <perpendicular axis theorem>. The point need not be the <centre of mass>, and the axes need not be <principal axes>.