Convex curve has at least four vertices, points that are local minima or local maxima of curvature. A curve "C" is convex if and only if there are no three different points in "C" such that the tangents in these points are parallel. Proof: ⇒ If there are three parallel tangents, then one of them, say "L", must be between the other two. This means that "C" lies on both sides of "L", so it cannot be convex. ⇐ If "C" is not convex, then by definition there is point "p" on "C" such that the tangent line at "p" (call it
Crepuscular rays Crepuscular rays Crepuscular rays (more commonly known as sunbeams, sun rays, splintered light, or god rays), in atmospheric optics, are rays of sunlight that appear to radiate from the point in the sky where the Sun is located. Shining through openings in clouds (particularly stratocumulus) or between other objects, these columns of sunlit particulates are separated by darker cloud-shadowed volumes. Despite seeming to converge toward the light source, the rays are in fact near-parallel shafts of sunlight. Their apparent convergence is a perspective effect. This phenomenon mimics the way parallel railway lines or long hallways, for example, seem to seek