The Blaschke Boundary Identifier is a Java applet that visualizes the following result:
Daepp - Gorkin - Mortini (2002): Let B be a Blaschke product of degree 3 with one zero at the origin. The line joining any two points on the unit circle identified by B is tangent to the ellipse with foci at the two zeros of B not at the origin.
See also the original article, Ulrich Daepp, Pamela Gorkin and Raymond Mortini, Ellipses and finite Blaschke products, Amer. Math. Monthly 109 (2002), no. 9, 785-795 (JSTOR).
In this applet you can drag the zeros around, and add or remove zeros using your mouse.