Projecting Graphs of Real-Valued Functions of a Real Variable to the Riemann Sphere

This Demonstration projects the graph of the real-valued function (blue) to a curve (pink) on a Riemann sphere. The Riemann sphere's south pole is zero and its north pole is infinity; it is tangent at its south pole to the - plane at the origin. You can hide the plane and projection line from the graph to the curve with "sphere only".