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
Anticrepuscular rays Anticrepuscular rays Anticrepuscular rays, or antisolar rays, are atmospheric optical phenomena similar to crepuscular rays, but appear opposite of the Sun in the sky. Anticrepuscular rays are nearly parallel, but appear to converge toward the antisolar point due to linear perspective. Anticrepuscular rays are most frequently visible around sunrise or sunset. Appearing to radiate from the Sun, crepuscular rays usually look much brighter than anticrepuscular rays. This is because the atmospheric light scattering making the crepuscular rays visible occurs at low angles to the horizon (see Mie theory). Although anticrepuscular rays appear to converge toward the antisolar point, the convergence