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]

# Dictionary Definition

### Verb

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- Plural of coordinate
- Coordinated clothes.

#### Translations

- French: coordonnées f|p
- Italian: coordinati m|p

### Verb

coordinates- 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:

- Continuous functions on topological spaces;
- Smooth functions on smooth manifolds;
- Measurable functions on measure spaces;
- Rational functions on algebraic varieties;
- Linear functionals on vector spaces.

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)

- r1, ..., rn.

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:- The Cartesian coordinate system (also called the "rectangular coordinate system"), which, for three-dimensional flat space, uses three numbers representing distances.
- Curvilinear coordinates are a generalization of coordinate systems generally; the system is based on the intersection of curves.
- The polar
coordinate systems:
- Circular coordinate system (commonly referred to as the polar coordinate system) represents a point in the plane by an angle and a distance from the origin.
- Cylindrical coordinate system represents a point in space by an angle, a distance from the origin and a height.
- Spherical coordinate system represents a point in space with two angles and a distance from the origin.

- Plücker coordinates are a way of representing lines in 3D Euclidean space using a six-tuple of numbers as homogeneous coordinates.
- Generalized coordinates are used in the Lagrangian treatment of mechanics.
- Canonical coordinates are used in the Hamiltonian treatment of mechanics.
- Intrinsic coordinates describe a point upon a curve by the length of the curve to that point and the angle the tangent to that point makes with the x-axis.
- Parallel coordinates visualise a point in n-dimensional space as a polyline connecting points on n vertical lines.

## 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

- Hexagonal Coordinate System
- Coordinates of a point Interactive tool to explore coordinates of a point

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