Ellipses and Finite Blaschke Products
| In a recent article appeared in the
American Mathematical Monthly, Daepp, Gorkin and Mortini
proved the following theorem: Let B
be a Blaschke product of degree three with distict zeros
at the points 0, a, b.
For l
on
the unit circle, let z1,
z2,
z3
denote the points mapped to l under B. Then the sides of the
triangle z1,
z2,
z3 are
tangent to the ellipse with equation |
|w-a|+|w-b|=|1-conj(a)*b|
|
| This Java applet shows how the ellipse changes moving the zeros a and b (i.e. by dragging the two dots) inside the unit circle. |