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...

returns to the origin; etc. There are however different coordinate systems for hyperbolic plane geometry. All are based around choosing a point (the origin)...

In mathematics, hyperbolic coordinates are a method of locating points in quadrant I of the Cartesian plane { ( x , y )   :   x > 0 ,   y > 0   } = Q...

point. The elliptic plane may be further defined by adding a metric to the real projective plane. One may also conceive of a hyperbolic plane, which obeys...

fundamental plane. The following table lists the common coordinate systems in use by the astronomical community. The fundamental plane divides the celestial...

the orbital plane as the x y {\displaystyle xy} plane is known as the perifocal coordinate system. For launch vehicles and artificial satellites, the...

a paraboloid made 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...

In geometry, the elliptic coordinate system is a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal ellipses and hyperbolae...

can also be curved, for example the sphere and hyperbolic plane, sufficiently small portions of which appear like the flat plane, but on which straight...

orthogonal coordinate system based on families of ellipses and hyperbolas. Hyperbolic growth Hyperbolic partial differential equation Hyperbolic sector Hyperboloid...

Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane. The set R 2 {\displaystyle \mathbb {R} ^{2}} of the ordered pairs...

computational geometry. Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two...

hyperboloid, one can choose a Cartesian coordinate system such that the hyperboloid is defined by one of the following equations: x 2 a 2 + y 2 b 2 −...

barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a...

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)...

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...

CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), Linear CORDIC, Hyperbolic CORDIC...

that are hyperbolic-orthogonal remain in that relation when the plane is subjected to hyperbolic rotation. An axiomatic treatment of plane affine geometry...

Branched manifolds first appeared in the dynamical systems theory, in connection with one-dimensional hyperbolic attractors constructed by Smale and were...

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...

geometry Riemannian geometry Symplectic geometry Non-Euclidean plane geometry Angle excess Hyperbolic geometry Pseudosphere Tractricoid Elliptic geometry Spherical...

, Euclidean) plane is a surface of constant zero curvature, and a hyperbolic plane is a surface of constant negative curvature. Einstein's general theory...

plane is said to be elliptic or hyperbolic according as each of its lines contains no point at infinity or two points at infinity. The elliptic plane...

instrumental in the validation of speculations of Lobachevski and Bolyai concerning hyperbolic geometry by providing models for the hyperbolic plane: for example...

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...

TDOA systems. TDOA systems are explicitly hyperbolic while TOA systems are implicitly hyperbolic. Pseudo-range multilateration navigation systems have...

The averages are well defined for ergodic systems and a more detailed understanding has been worked out for hyperbolic systems. Understanding the probabilistic...

Rindler coordinates are a coordinate system used in the context of special relativity to describe the hyperbolic acceleration of a uniformly accelerating...

. The pair ( M , g ) {\displaystyle (M,g)} is typically called the hyperbolic plane and has Killing vector field ∂ x {\displaystyle \partial _{x}} (using...

characterizing the orientation of the coordinate system x̂, ŷ, ẑ from the inertial coordinate frame Î, Ĵ, K̂ where: Î, Ĵ is in the equatorial plane of the central...