Mobius transforms are transformations of the function f(z) = (az + b)/(cz + d), where a,b,c,d,z are complex variables.
Mobius transformations are defined on the extended complex plane that is augmented by infinity.
Stereographic Projection - Mappying that projects a sphere onto a plane, where the projection is defined at every point but the projection point (Used to picture the sphere as a plane)
-Stereographic Projections will preserve angles at which curves cross each other, but not area
Mobius transformations can be obtained by obtaining a stereographic projection, then rotating/moving to a different orientation in space, and project the sphere back to a plane (drawing a line from the pole of infinity to the plane)
Riemann Sphere - Model of an extended complex plane in the form of a sphere, consisting of complex numbers and infinity