AskDefine | Define coordinates

Dictionary Definition

co-ordinates (See coordinate)
adj : of equal importance, rank, or degree n : a number that identifies a position relative to an axis [syn: co-ordinate]

Verb

1 bring order and organization to; "Can you help me organize my files?" [syn: organize, organise]
2 bring into common action, movement, or condition; "coordinate the painters, masons, and plumbers"; "coordinate his actions with that of his colleagues"; "coordinate our efforts"
3 be co-ordinated; "These activities co-ordinate well"
4 bring (components or parts) into proper or desirable coordination correlation; "align the wheels of my car"; "ordinate similar parts" [syn: align, ordinate] [also: co-ordinating, co-ordinates, co-ordinated, co-ordinate]

User Contributed Dictionary

English

Noun

coordinates
  1. Plural of coordinate
  2. Coordinated clothes.

Translations

Verb

coordinates
  1. third-person singular of coordinate

Extensive Definition

In mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space. "Scalars" in many cases means real numbers, but, depending on context, can mean complex numbers or elements of some other commutative ring. For complicated spaces, it is often not possible to provide one consistent coordinate system for the entire space. In this case, a collection of coordinate systems, called charts, are put together to form an atlas covering the whole space. A simple example (which motivates the terminology) is the surface of the earth.
Although a specific coordinate system is useful for numerical calculations in a given space, the space itself is considered to exist independently of any particular choice of coordinates. From this point of view, a coordinate on a space is simply a function from the space (or a subset of the space) to the scalars. When the space has additional structure, one restricts attention to the functions which are compatible with this structure. Examples include: The coordinates on a space transform naturally (by pullback) under the group of automorphisms of the space, and the set of all coordinates is a commutative ring called the coordinate ring of the space.
In informal usage, coordinate systems can have singularities: these are points where one or more of the coordinates is not well-defined. For example, the origin in the polar coordinate system (r,θ) on the plane is singular, because although the radial coordinate has a well-defined value (r = 0) at the origin, θ can be any angle, and so is not a well-defined function at the origin.

Examples

The prototypical example of a coordinate system is the Cartesian coordinate system, which describes a point P in the Euclidean space Rn by an n-tuple
P = (r1, ..., rn)
of real numbers
r1, ..., rn.
These numbers r1, ..., rn are called the coordinates linear polynomials of the point P.
If a subset S of a Euclidean space is mapped continuously onto another topological space, this defines coordinates in the image of S. That can be called a parametrization of the image, since it assigns numbers to points. That correspondence is unique only if the mapping is bijective.
The system of assigning longitude and latitude to geographical locations is a coordinate system. In this case the parametrization fails to be unique at the north and south poles.

Defining a coordinate system based on another one

In geometry and kinematics, coordinate systems are used not only to describe the (linear) position of points, but also to describe the angular position of axes, planes, and rigid bodies. In the latter case, the orientation of a second (typically referred to as "local") coordinate system, fixed to the node, is defined based on the first (typically referred to as "global" or "world" coordinate system). For instance, the orientation of a rigid body can be represented by an orientation matrix, which includes, in its three columns, the Cartesian coordinates of three points. These points are used to define the orientation of the axes of the local system; they are the tips of three unit vectors aligned with those axes.

Transformations

A coordinate transformation is a conversion from one system to another, to describe the same space.
With every bijection from the space to itself two coordinate transformations can be associated:
  • such that the new coordinates of the image of each point are the same as the old coordinates of the original point (the formulas for the mapping are the inverse of those for the coordinate transformation)
  • such that the old coordinates of the image of each point are the same as the new coordinates of the original point (the formulas for the mapping are the same as those for the coordinate transformation)
For example, in 1D, if the mapping is a translation of 3 to the right, the first moves the origin from 0 to 3, so that the coordinate of each point becomes 3 less, while the second moves the origin from 0 to -3, so that the coordinate of each point becomes 3 more.

Systems commonly used

Some coordinate systems are the following:

A list of common coordinate systems

The following coordinate systems all have the properties of being orthogonal coordinate systems, that is the coordinate surfaces meet at right angles.

Geographical systems

Geography and cartography utilize various geographic coordinate systems to map positions on the 3-dimensional globe to a 2-dimensional document.
The Global Positioning System uses the WGS84 coordinate system.
The Universal Transverse Mercator (UTM) and Universal Polar Stereographic (UPS) coordinate systems both use a metric-based cartesian grid laid out on a conformally projected surface to locate positions on the surface of the Earth. The UTM system is not a single map projection but a series of map projections, one for each of sixty zones. The UPS system is used for the polar regions, which are not covered by the UTM system.
During medieval times, the stereographic coordinate system was used for navigation purposes. The stereographic coordinate system was superseded by the latitude-longitude system, and more recently, the Global Positioning System.
Although no longer used in navigation, the stereographic coordinate system is still used in modern times to describe crystallographic orientations in the field of materials science.

Astronomical systems

Coordinate systems on the sphere are particularly important in astronomy: see astronomical coordinate systems.

External links

coordinates in Afrikaans: Koördinaatstelsel
coordinates in Asturian: Coordenada
coordinates in Bulgarian: Координата
coordinates in Catalan: Coordenada
coordinates in Czech: Soustava souřadnic
coordinates in Danish: Koordinatsystem
coordinates in German: Koordinatensystem
coordinates in Modern Greek (1453-): Σύστημα συντεταγμένων
coordinates in Spanish: Sistema de coordenadas
coordinates in Esperanto: Koordinatsistemo
coordinates in French: Système de coordonnées
coordinates in Scottish Gaelic: Siostaman cho-chomharran
coordinates in Galician: Sistema de coordenadas
coordinates in Korean: 좌표계
coordinates in Italian: Sistema di riferimento
coordinates in Hebrew: קואורדינטות
coordinates in Luxembourgish: Koordinate-system
coordinates in Lithuanian: Koordinačių sistema
coordinates in Dutch: Coördinaat
coordinates in Japanese: 座標
coordinates in Norwegian: Koordinatsystem
coordinates in Polish: Układ współrzędnych
coordinates in Portuguese: Sistema de coordenadas
coordinates in Russian: Система координат
coordinates in Slovenian: Koordinatni sistem
coordinates in Albanian: Sistemi koordinativ
coordinates in Slovak: Sústava súradníc
coordinates in Finnish: Koordinaatisto
coordinates in Swedish: Koordinatsystem
coordinates in Tamil: பகுமுறை வடிவவியல்
coordinates in Turkish: Küresel koordinat sistemi
coordinates in Chinese: 坐標系統
coordinates in Ukrainian: Системи координат

Synonyms, Antonyms and Related Words

Cartesian coordinates, abscissa, altitude, azimuth, boundaries, bounds, bourns, circumference, circumscription, compass, confines, cylindrical coordinates, declination, edges, equator coordinates, fringes, latitude, limitations, limits, longitude, marches, metes, metes and bounds, ordinate, outlines, outskirts, pale, parameters, perimeter, periphery, polar coordinates, right ascension, skirts, verges
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