Convex curve itself. A closed regular plane simple curve "C" is convex "if and only if" its curvature is either always non-negative or always non-positive—i.e., if and only if the "turning angle" (the angle of the tangent to the curve) is a weakly monotone function of the parametrization of the curve. Proof: ⇐ If "C" is not convex, then by the parallel tangents lemma there are three points {"p","q1","q2"} such that the tangents at these points are parallel. At least two must have their signed tangents pointing in the same direction. Without loss of generality, assume that these points are "q1" and
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