Chapter 9 Conformal Mapping
The terminology “conformal mapping” should have a familiar sound. In 1569 the Flemish cartographer Gerardus Mercator (1512–1594) devised a cylindrical map projection that preserves angles. The Mercator projection is still used today for world maps. Another map projection known to the ancient Greeks is the stereographic projection. It is also conformal (i.e., angle preserving), and we introduced it in Chapter 2 when we defined the Riemann sphere. In complex analysis a function preserves angles if and only if it is analytic or anti-analytic (i.e., the conjugate of an analytic function). A significant result, known as Riemann mapping theorem, states that any simply connected domain (other than the entire complex plane) can be mapped conformally onto the unit disk.
