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Upper half-plane

In mathematics, the upper half-plane, ⁠ H , {\displaystyle {\mathcal {H}},} ⁠ is the set of points ⁠ ( x , y ) {\displaystyle (x,y)} ⁠ in the Cartesian plane with ⁠ y > 0. {\displaystyle y>0.} ⁠ The lower half-plane is the set of points ⁠ ( x , y ) {\displaystyle (x,y)} ⁠ with ⁠ y < 0 {\displaystyle y<0} ⁠ instead. Arbitrarily oriented half-planes can be…

Art, Complex plane & Generalizations

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Affine geometry

Inversive geometry

Metric geometry

Complex plane

Generalizations

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Upper half-plane

Nodes57
Edges56
Triples24
Avg. degree1.96
Density0.035088
Components1

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Upper half-plane

Top relations

related to References · 7
Upper half-plane → Eric, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, MathWorld, Weisstein, Wikisource-logo
related to Generalizations · 6
Upper half-plane → Hilbert, In, One, Riemannian, Siegel, Yet
related to Metric geometry · 5
Upper half-plane → By, Distances, In, Poincaré, The
related to Complex plane · 4
Upper half-plane → Cartesian, Mathematicians, The, When
is a · 1
Upper half-plane → 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
related to Affine geometry · 1
Upper half-plane → The

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Important terminology

half-plane displaystyle upper mathcal points metric complex plane set space hyperbolic half-space affine geometry boundary cos circle poincaré modular half-planes

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Upper half-planeis auniversal 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 axis0.90text
Upper half-planerelated to Affine geometryThe0.60section
Upper half-planerelated to Complex planeMathematicians0.60section
Upper half-planerelated to Complex planeCartesian0.60section
Upper half-planerelated to Complex planeThe0.60section
Upper half-planerelated to Complex planeWhen0.60section
Upper half-planerelated to GeneralizationsOne0.60section
Upper half-planerelated to GeneralizationsRiemannian0.60section
Upper half-planerelated to GeneralizationsIn0.60section
Upper half-planerelated to GeneralizationsHilbert0.60section
Upper half-planerelated to GeneralizationsYet0.60section
Upper half-planerelated to GeneralizationsSiegel0.60section

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