Lower half-plane

Lower half-plane

In mathematics, the lower half-plane H is the set of complex numbers

:mathbb{H} = {x + iy ;| y < 0; x, y in mathbb{R} }

with positive imaginary part "y". Other names are hyperbolic plane, Poincaré plane and Lobachevsky plane, particularly in texts by Russian authors. Some authors prefer the symbol mathfrak{h}.

ee also

* Upper half-plane
* Cusp neighborhood
* Fuchsian group
* Fundamental domain
* Hyperbolic geometry
* Kleinian group
* Modular group
* Poincaré metric
* Riemann surface
* Schwarz-Ahlfors-Pick theorem

External links

* [http://www.hqbach.net/index.php?item=Poincare%20Half-Plane%20Model Visual presentation of the upper half-plane]


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Upper half-plane — In mathematics, the upper half plane H is the set of complex numbers with positive imaginary part y: The term is associated with a common visualization of complex numbers with points in the plane endowed with Cartesian coordinates, with the Y… …   Wikipedia

  • Half-space — For other uses, see Half space (disambiguation). In geometry, a half space is either of the two parts into which a plane divides the three dimensional euclidean space. More generally, a half space is either of the two parts into which a… …   Wikipedia

  • half tube —    1. An inverted channel with semi circular cross section seen in cave passage ceilings, most clearly where the ceiling is an uneroded bedding surface. The half tube originates as part of a phreatic tube guided by the bedding plane, and the… …   Lexicon of Cave and Karst Terminology

  • half-tube —    1. An inverted channel with semi circular cross section seen in cave passage ceilings, most clearly where the ceiling is an uneroded bedding surface. The half tube originates as part of a phreatic tube guided by the bedding plane, and the… …   Lexicon of Cave and Karst Terminology

  • Plane (Dungeons & Dragons) — Ethereal plane redirects here. For the mystical concept, see Etheric plane. The planes of the Dungeons Dragons roleplaying game constitutes the multiverse in which the game takes place. In the earliest versions of Dungeons Dragons, the concept of …   Wikipedia

  • Plane (Magic: The Gathering) — In Magic: The Gathering, planes are parallel universes in the Multiverse (which used to be referred to as Dominia.) Planes are often confused with planets by Magic players, because most planes are named after their primary planets. The two main… …   Wikipedia

  • Lower limit topology — In mathematics, the lower limit topology or right half open interval topology is a topology defined on the set R of real numbers; it is different from the standard topology on R and has a number of interesting properties. It is the topology… …   Wikipedia

  • Complex plane — Geometric representation of z and its conjugate in the complex plane. The distance along the light blue line from the origin to the point z is the modulus or absolute value of z. The angle φ is the argument of z. In mathematics …   Wikipedia

  • Sawing a woman in half — is a generic name for a number of different stage magic tricks in which a person (traditionally a female assistant) is apparently sawn or divided into two or more pieces. Contents 1 History 2 Effects and variations 2.1 The Selbit sawing …   Wikipedia

  • Snakes on a Plane — For the first single from Cobra Starship, see Snakes on a Plane (Bring It). Snakes on a Plane …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”