Coordinate systems for the hyperbolic plane information
In the hyperbolic plane, as in the Euclidean plane, each point can be uniquely identified by two real numbers. Several qualitatively different ways of coordinatizing the plane in hyperbolic geometry are used.
This article tries to give an overview of several coordinate systems in use for the two-dimensional hyperbolic plane.
In the descriptions below the constant Gaussian curvature of the plane is −1. Sinh, cosh and tanh are hyperbolic functions.
and 25 Related for: Coordinate systems for the hyperbolic plane information
of coordinatizingtheplane in hyperbolic geometry are used. This article tries to give an overview of several coordinatesystems in use forthe two-dimensional...
fundamental plane. The following table lists the common coordinatesystems in use by the astronomical community. The fundamental plane divides the celestial...
section of a paraboloid by a plane parallel to the axis of symmetry is a parabola. The paraboloid is hyperbolic if every other plane section is either a hyperbola...
the orbital plane as the x y {\displaystyle xy} plane is known as the perifocal coordinatesystem. For launch vehicles and artificial satellites, the...
(have the same area), among many other topics. Later, theplane was described in a so-called Cartesian coordinatesystem, a coordinatesystem that specifies...
adj. hyperbolic /ˌhaɪpərˈbɒlɪk/ ) is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution...
In geometry, the elliptic coordinatesystem is a two-dimensional orthogonal coordinatesystem in which thecoordinate lines are confocal ellipses and hyperbolae...
computational geometry. Usually the Cartesian coordinatesystem is applied to manipulate equations forplanes, straight lines, and circles, often in two...
barycentric coordinatesystem is a coordinatesystem in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a...
complex numbers in the complex plane, the same formula for one-dimensional points expressed as real numbers can be used, although here the absolute value...
hyperboloid, one can choose a Cartesian coordinatesystem such that the hyperboloid is defined by one of the following equations: x 2 a 2 + y 2 b 2 −...
modelling power of hyperbolic versors operating on the split-complex number plane, and in 1891 he introduced hyperbolic quaternions to extend the concept to 4-space...
. The pair ( M , g ) {\displaystyle (M,g)} is typically called thehyperbolicplane and has Killing vector field ∂ x {\displaystyle \partial _{x}} (using...
charge located near the corner of two conducting planes separated by a certain angle (where z {\displaystyle z} is the complex coordinate of a point in 2-space)...
instrumental in the validation of speculations of Lobachevski and Bolyai concerning hyperbolic geometry by providing models forthehyperbolicplane: for example...
that are hyperbolic-orthogonal remain in that relation when theplane is subjected to hyperbolic rotation. An axiomatic treatment of plane affine geometry...
The averages are well defined for ergodic systems and a more detailed understanding has been worked out forhyperbolicsystems. Understanding the probabilistic...
intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though...
characterizing the orientation of thecoordinatesystem x̂, ŷ, ẑ from the inertial coordinate frame Î, Ĵ, K̂ where: Î, Ĵ is in the equatorial plane of the central...
Rindler coordinates are a coordinatesystem used in the context of special relativity to describe thehyperbolic acceleration of a uniformly accelerating...
points they represent. A two-dimensional coordinatesystem on the stereographic plane is an alternative setting for spherical analytic geometry instead of...
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