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. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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Named for Bernhard Riemann and arising from his work on complex analysis in the 1850s.
Source Riemann Sphere (Wikipedia)
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Source Riemann Sphere (Wikipedia)
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1. Riemann Sphere (Wikipedia)
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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.
- In Branch: Complex Analysis
- Associated With: Bernhard Riemann
View the Source 2. Riemann (MacTutor History of Mathematics)
Biography, Gottingen periodQuote, Biography, Gottingen period
In 1849 he returned to Gottingen and his Ph.D. thesis, supervised by Gauss, was submitted in 1851.
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