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- Upper_half-plane abstract "In mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part:The term arises from a common visualization of the complex number x + iy as the point (x,y) in the plane endowed with Cartesian coordinates. When the Y-axis is oriented vertically, the "upper half-plane" corresponds to the region above the X-axis and thus complex numbers for which y > 0.It is the domain of many functions of interest in complex analysis, especially modular forms. The lower half-plane, defined by y < 0, is equally good, but less used by convention. The open unit disk D (the set of all complex numbers of absolute value less than one) is equivalent by a conformal mapping to H (see "Poincaré metric"), meaning that it is usually possible to pass between H and D.It also plays an important role in hyperbolic geometry, where the Poincaré half-plane model provides a way of examining hyperbolic motions. The Poincaré metric provides a hyperbolic metric on the space.The uniformization theorem for surfaces states that the upper half-plane is the universal covering space of surfaces with constant negative Gaussian curvature.The closed upper half-plane is the union of the upper half-plane and the real axis. It is the closure of the upper half-plane.".
- Upper_half-plane wikiPageID "287826".
- Upper_half-plane wikiPageRevisionID "606033320".
- Upper_half-plane hasPhotoCollection Upper_half-plane.
- Upper_half-plane title "Upper Half-Plane".
- Upper_half-plane urlname "UpperHalf-Plane".
- Upper_half-plane subject Category:Complex_analysis.
- Upper_half-plane subject Category:Differential_geometry.
- Upper_half-plane subject Category:Hyperbolic_geometry.
- Upper_half-plane subject Category:Modular_forms.
- Upper_half-plane subject Category:Number_theory.
- Upper_half-plane type Abstraction100002137.
- Upper_half-plane type Form106290637.
- Upper_half-plane type LanguageUnit106284225.
- Upper_half-plane type ModularForms.
- Upper_half-plane type Part113809207.
- Upper_half-plane type Relation100031921.
- Upper_half-plane type Word106286395.
- Upper_half-plane comment "In mathematics, the upper half-plane H is the set of complex numbers with positive imaginary part:The term arises from a common visualization of the complex number x + iy as the point (x,y) in the plane endowed with Cartesian coordinates. When the Y-axis is oriented vertically, the "upper half-plane" corresponds to the region above the X-axis and thus complex numbers for which y > 0.It is the domain of many functions of interest in complex analysis, especially modular forms.".
- Upper_half-plane label "Bovenhalfvlak".
- Upper_half-plane label "Meio plano superior".
- Upper_half-plane label "Upper half-plane".
- Upper_half-plane label "上半平面".
- Upper_half-plane sameAs 上半平面.
- Upper_half-plane sameAs 상반평면.
- Upper_half-plane sameAs Bovenhalfvlak.
- Upper_half-plane sameAs Meio_plano_superior.
- Upper_half-plane sameAs m.01q7vs.
- Upper_half-plane sameAs Q3258885.
- Upper_half-plane sameAs Q3258885.
- Upper_half-plane sameAs Upper_half-plane.
- Upper_half-plane wasDerivedFrom Upper_half-plane?oldid=606033320.
- Upper_half-plane isPrimaryTopicOf Upper_half-plane.