anharmonic ratio | anharmonic section | cross-ratio

If a, b, c, and d are points in the extended complex plane C^*, their cross ratio, also called the cross-ratio, anharmonic ratio, and anharmonic section, is defined by [a, b, c, d] congruent ((a - b)(c - d))/((a - d)(c - b)). Here if a = d, the result is infinity, and if one of a, b, c, or d is infinity, then the two terms on the right containing it are cancelled. For a linear fractional transformation f, [a, b, c, d] = [f(a), f(b), f(c), f(d)].

bivalent range | equicross | harmonic range | homographic | Möbius transformation | separation