Convex set polygon is sometimes called a concave polygon, and some sources more generally use the term "concave set" to mean a non-convex set, but most authorities prohibit this usage. The complement of a convex set, such as the epigraph of a concave function, is sometimes called a "reverse convex set", especially in the context of mathematical optimization. If is a convex set in -dimensional space, then for any collection of , , -dimensional vectors in , and for any nonnegative numbers such that , then one has: A vector of this type is known as a convex combination of . The
Lens clock clock can be used if a dial thickness gauge is not available. To do this, the contact lens is placed concave side up on a table or other hard surface. The lens clock is then brought down on it such that the center prong contacts the lens as close to its center as possible, and the outer prongs rest on the table. The thickness of the lens is then the sagitta formula_4 in the formula above, and can be calculated from the optical power reading, if the distance between the outer prongs is known. Lens clock A lens clock is