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...

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...

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

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...

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

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...

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...

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

to modify the Euclidean parallel postulate is to assume that there are no parallel lines in a plane. Unlike the situation with hyperbolic geometry, where...

{\displaystyle a} in the x y {\displaystyle xy} plane of the toroidal coordinate system; the z {\displaystyle z} -axis is the axis of rotation. The focal ring is...

the length of its semi-minor axis. In the coordinate system with origin at the ellipse's center and x-axis aligned with the major axis, points on the...

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

methods. For more, see Euclidean space. Below are images of the above-mentioned systems. Cartesian coordinate system Cylindrical coordinate system Spherical...

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...

considered—spherical geometry and hyperbolic plane geometry; in each case, as in the Euclidean case for non-right triangles, the result replacing the Pythagorean theorem...

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

approaches zero, i.e. for spherical triangles as which are infinitesimal in proportion to the radius of the sphere. In the hyperbolic plane, given a triangle...

mathematical space in which location can be specified with a single coordinate. An example is the number line, each point of which is described by a single real...

 'the directions') is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system....

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

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

elliptic pencil is another elliptic pencil, the inversion of a hyperbolic pencil is another hyperbolic pencil, and the inversion of a parabolic pencil is another...

tiling) is a tiling of the hyperbolic plane, resembling a quadtree over the Poincaré half-plane model of the hyperbolic plane. The tiles are congruent,...

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

pointsymmetric to the origin, symmetric to the coordinate planes and rotational symmetric to the z-axis and symmetric to any plane containing the z-axis, in...

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...