Stereographic projection

Summary

Stereographic projection maps the unit sphere minus one point, its north pole, bijectively onto a plane, see the definition. Sending the north pole to a point at infinity makes the sphere a model of the Riemann sphere $\C \cup \set{\infty}$. The map preserves angles and sends circles on the sphere to circles or lines in the plane. It is the bridge between the geometry of the sphere and complex analysis on the extended plane.