Karl Jones: /* External links */

2016-09-13T02:18:53Z

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Karl Jones at 02:18, 13 September 2016

2016-09-13T02:18:17Z

Karl Jones: Created page with "A '''Cartesian coordinate system''' is a coordinate system that specifies each point uniquely in a plane by a pair of Number|nu..."

2016-09-13T02:15:54Z

Created page with "A '''Cartesian coordinate system''' is a coordinate system that specifies each point uniquely in a plane by a pair of Number|nu..."

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A '''Cartesian coordinate system''' is a [[coordinate system]] that specifies each [[Point (geometry)|point]] uniquely in a [[Plane (geometry)|plane]] by a pair of [[Number|numerical]] coordinates, which are the [[Sign (mathematics)|signed]] distances to the point from two fixed [[perpendicular]] directed lines, measured in the same [[Unit vector|unit of length]].

== Description ==

Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its [[Origin (mathematics)|origin]], usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.

Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is (x − a)2 + (y − b)2 = r2 where a and b are the coordinates of the center (a, b) and r is the radius.

The invention of Cartesian coordinates in the 17th century by [[René Descartes]] (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as [[Curve|curves]]) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2, centered at the origin of the plane, may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.

Cartesian coordinates are the foundation of [[analytic geometry]], and provide enlightening geometric interpretations for many other branches of mathematics, such as [[linear algebra]], [[complex analysis]], [[differential geometry]], [[multivariate calculus]], [[group theory]], and more.

A familiar example is the concept of the graph of a [[Function (mathematics)|function]].

Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, [[physics]], [[engineering]], and many more. They are the most common coordinate system used in [[computer graphics]], [[computer-aided geometric design]], and other geometry-related [[data processing]].

== See also ==

* [[Horizontal and vertical]]
* [[Jones diagram]], which plots four variables rather than two.
* [[Orthogonal coordinates]]
* [[Polar coordinate system]]
* [[Spherical coordinate system]]

== External links ==

* [[https://en.wikipedia.org/wiki/Cartesian_coordinate_system Cartesian coordinate system] @ Wikipedia

[[Category:Geometry]]
[[Category:Mathematics]]

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 == See also ==
 * [[Horizontal and vertical]]
 * [[Jones diagram]], which plots four variables rather than two.

Cartesian coordinate system - Revision history

Karl Jones: /* External links */

Karl Jones at 02:18, 13 September 2016

Karl Jones: Created page with "A '''Cartesian coordinate system''' is a coordinate system that specifies each point uniquely in a plane by a pair of Number|nu..."