Riemann sphere

English dictionary entry

Meanings

noun

The complex numbers extended with the number ∞; the complex plane (representation of the complex numbers as a Euclidean plane) extended with a single idealised point at infinity and consequently homeomorphic to a sphere in 3-dimensional Euclidean space.
The 2-sphere embedded in Euclidean three-dimensional space and often represented as a unit sphere, regarded as a homeomorphic representation of the extended complex plane and thus the extended complex numbers.

Riemann sphere Riemann spheres

Named after German mathematician Bernhard Riemann.

extended complex numbers closed complex plane extended complex plane

Argand plane complex manifold complex plane complex projective line Riemann surface

Italian: sfera di Riemann Polish: sfera Riemanna Russian: сфе́ра Ри́мана

This entry uses open data from Wiktionary (CC BY-SA/GFDL). Word forms are used for search and are not indexed as separate pages.

Back to search All on R Russian dictionary Dahl dictionary