Riemann sphere

Uncommon card · No. 183565

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the complex plane plus one point at infinity. This extended plane represents the extended complex numbers, that is, the complex numbers plus a value ∞ {\displaystyle \infty } for infinity. With the Riemann model, the point ∞ {\displaystyle \infty } is near to very large numbers, just as the point 0 {\displaystyle 0} is near to very small numbers. The extended complex numbers are useful in complex analysis because they allow for division by zero in some circumstances, in a way that makes expressions such as 1 / 0 = ∞ {\displaystyle 1/0=\infty } well-behaved. For example, any rational function on the complex plane can be...

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