Riemann Sphere

The Riemann sphere is a model of the extended complex plane, the ordinary complex numbers together with a single additional point at infinity, named for Bernhard Riemann and arising from his work on complex analysis in the 1850s. The point at infinity plays a role analogous to the role zero plays for very small numbers, allowing expressions such as one divided by zero to be given a well-defined meaning as that point. The sphere can be constructed from the complex plane by stereographic projection, a map that wraps the whole infinite plane around a sphere so that every point of the plane, and the single point at infinity, corresponds to exactly one point on the sphere's surface.