Mathematics Atlas

How Proof Is Made
Sign In
Text size
100%
Theme
Mathematical Object

Riemann Sphere

Analysis

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/

Facts
Classification
Object Kind
Space 1
Origin Year
1851 2
Connections

Associated With

Bernhard Riemann, Mathematicians

Named for Bernhard Riemann and arising from his work on complex analysis in the 1850s.

Source Riemann Sphere (Wikipedia)

In Branch

Source Riemann Sphere (Wikipedia)
Sources
1. Riemann Sphere (Wikipedia)
Wikimedia Foundation
  • Lead section
    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 period
Quote, Biography, Gottingen period
In 1849 he returned to Gottingen and his Ph.D. thesis, supervised by Gauss, was submitted in 1851.
View the Source
Comments (0)
No comments yet. Be the first to share a thought.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.