Meaning of stereographic projection | Babel Free

Definitions

A function that maps a sphere onto a plane; especially, the map generated by projecting each point of the sphere from the sphere's (designated) north pole to a point on the plane tangent to the south pole.

Examples

“1974 [Prentice-Hall], Richard A. Silverman, Complex Analysis with Applications, Dover, 1984, Unaltered republication, page 19, Thus we see that stereographic projection establishes a one-to-one correspondence between the extended complex plane and the Riemann sphere.”

“1991, E. J. F. Primrose (translator), Simeon Ivanov (editor of translation), A. T. Fomenko, A. A. Tuzhilin, Elements of the Geometry and Topology of Minimal Surfaces in Three-Dimensional Space, American Mathematical Society, page 67, Proposition 2. The stereographic projection π_N:S²→Oxy of the sphere S² onto the xy-plane from the North Pole N preserves the angles between tangent vectors. Thus, the coordinates specified on S²⧵N by the stereographic projection π_N are isothermal.”

“Before we can recognize such patterns confidently, we need to know whether the stereographic projection faithfully represents the true clustering of directions in space.”

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