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coordinates

Coordinates are distances or angles, represented by numbers, that uniquely identify points on surfaces of two dimensions (2D) or in space of three dimensions ( 3D ). There are several coordinate schemes commonly used by mathematicians, scientists, and engineers.

Cartesian coordinates , also called rectangular coordinates, have two or three straight-line axes that define the positions of points in 2D or 3D. All scales are linear; that is, each scale is graduated in increments of uniform size.

Another coordinate system, semilog coordinates , define the positions of points in 2D. One scale is linear and the other is logarithmic (graduated in increments corresponding to the logarithm of the displacement). A similar system, log-log coordinates , is used to define the sitions of points in 2D, but in this scheme, both scales are logarithmic.

In another system, polar coordinates define the positions of points in 2D, according to displacement (radius) from a central origin, and the angular displacement (angle) from a reference axis emanating from the origin. The radial axis is usually linear, but in some polar graphs it is logarithmic. The angle can be specified in degree s or radian s, and can be measured clockwise or counterclockwise from the reference axis.

Polar coordinates extended into 3D become cylindrical coordinates by the addition of an elevation axis, passing through the origin and perpendicular to the polar plane. The elevation axis is usually linear, but in some instances it is logarithmic.

The azimuth and elevation , or az-el, coordinate system defines a direction in 3D space with respect to a chosen origin point, by specifying two angles. The well-known example of latitude and longitude are az-el coordinates of points on the earth's surface, with respect to an origin at the center of the earth, a latitude reference plane passing through the origin and the earth's equator, and a longitude reference plane passing through the origin and Greenwich, England.

The extension of latitude and longitude into the heavens is called celestial latitude and longitude . These az-el coordinates are determined from an origin at the center of the earth, a latitude reference plane passing through the origin and the earth's equator, and a longitude reference plane passing through the origin and Greenwich, England. A special form of celestial latitude and longitude is right ascension and declination , in which the longitude reference plane passes through the origin and the position of the sun in the sky at the vernal equinox (approximately March 21).

One can also create a system of spherical coordinates in which the positions of points in 3D use az-el angles and a radial distance from a chosen origin. The radial axis is usually linear, but it can be logarithmic.

More sophisticated coordinate systems than the aforementioned are encountered in advanced theory, applied science, and engineering. Such systems often involve four or more dimensions, axes that are curved, or axes that are neither linear nor logarithmic.

This was last updated in September 2005

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