A connected, rigid, flat object remains fixed on a convex, flat surface if and only if the object's center of gravity lies above the surface. The x-coordinate, for example, of the center of gravity of an object s can be calculated by (∫
sxds) / (∫
sds). Likewise, the y-coordinate can be expressed as (∫
syds) / (∫
sds). Note that the denominator of these expressions gives the area of s.
