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...

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...

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...

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...

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...

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

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...

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...

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...

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...

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...

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

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...

{\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...

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...

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 −...

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...

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

of a pseudo-Euclidean plane uses the term hyperbolic orthogonality. In the diagram, axes x′ and t′ are hyperbolic-orthogonal for any given ϕ {\displaystyle...

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...

projective plane is also a projective plane. The dual plane of a pappian plane is pappian and can also be coordinatized by homogeneous coordinates. A nondegenerate...

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