Every Mobius transformation can be constructed by stereographic projection of the complex plane onto a sphere, followed by a rigid motion of the sphere and projection back onto the plane, illustrated in the video Mobius Transformations Revealed. In this article we show that, for a given Mobius transformation and sphere, this representation is unique.

Author Bio

Robert Siliciano is an undergraduate student at Princeton University. Outside of mathematics, he is interested in economics and computer science.