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Definition: A stereographic projection maps points from the North Pole of a sphere onto the tangent plane at the South Pole and thus there corresponds to each point of the plane a definite point of the sphere. With the exception of the North Pole itself, each point of the sphere corresponds to exactly one point of the plane.
Source: Mathematical Analysis, second edition by Tom M. Apostol
Example: The complex numbers can be geographically represented using a stereographic projection.