Riemann sphere

The Riemann sphere is a mathematical model of the extended complex plane. The model is named after Bernhard Riemann. The extended complex plane is the plane of the complex numbers, plus a point at infinity. With this model, this point at infinity is "close" to very large numbers in the same way zero is "close" to very small ones. The extended complex numbers are useful for Complex analysis: in certain cases, the division by zero is "well-behaved", in the sense that dividing by zero gives this point at infinity. With this model, it is possible to change certain functions, so that they become continuous, which simplifies calculation.
In geometry, the Riemann sphere is a simple example of a Riemann surface. It is also one of the simplest complex manifolds.