# Cartesian coordinates

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Related to Cartesian coordinates: Cartesian equation

## Cartesian coordinates

(kärtē`zhən) [for René Descartes**Descartes, René**

, Lat.

*Renatus Cartesius,*1596–1650, French philosopher, mathematician, and scientist, b. La Haye. Descartes' methodology was a major influence in the transition from medieval science and philosophy to the modern era.

**.....**Click the link for more information. ], system for representing the relative positions of points in a plane or in space. In a plane, the point

*P*is specified by the pair of numbers (

*x,y*) representing the distances of the point from two intersecting straight lines, referred to as the

*x*-axis and the

*y*-axis. The point of intersection of these axes, which are called the coordinate axes, is known as the origin. In rectangular coordinates, the type most often used, the axes are taken to be perpendicular, with the

*x*-axis horizontal and the

*y*-axis vertical, so that the

*x*-coordinate, or abscissa, of

*P*is measured along the horizontal perpendicular from

*P*to the

*y*-axis (i.e., parallel to the

*x*-axis) and the

*y*-coordinate, or ordinate, is measured along the vertical perpendicular from

*P*to the

*x*-axis (parallel to the

*y*-axis). In oblique coordinates the axes are not perpendicular; the abscissa of

*P*is measured along a parallel to the

*x*-axis, and the ordinate is measured along a parallel to the

*y*-axis, but neither of these parallels is perpendicular to the other coordinate axis as in rectangular coordinates. Similarly, a point in space may be specified by the triple of numbers (

*x,y,z*) representing the distances from three planes determined by three intersecting straight lines not all in the same plane; i.e., the

*x*-coordinate represents the distance from the

*yz*-plane measured along a parallel to the

*x*-axis, the

*y*-coordinate represents the distance from the

*xz*-plane measured along a parallel to the

*y*-axis, and the

*z*-coordinate represents the distance from the

*xy*-plane measured along a parallel to the

*z*-axis (the axes are usually taken to be mutually perpendicular). Analogous systems may be defined for describing points in abstract spaces of four or more dimensions. Many of the curves studied in classical geometry can be described as the set of points (

*x,y*) that satisfy some equation

*f(x,y)*=0. In this way certain questions in geometry can be transformed into questions about numbers and resolved by means of analytic geometry

**analytic geometry,**

branch of geometry in which points are represented with respect to a coordinate system, such as Cartesian coordinates, and in which the approach to geometric problems is primarily algebraic.

**.....**Click the link for more information. .

## Cartesian Coordinates

a rectilinear system of coordinates in a plane or in space (usually with identical scales on both axes). R. Descartes himself used only a system of coordinates in a plane (generally oblique) in the work *Geometry* (1637). Often the Cartesian coordinates are understood to mean the rectangular Cartesian coordinates, while the general Cartesian coordinates are called an affine system of coordinates.

## cartesian coordinates

[kär′tē·zhən kō′ȯrd·nəts] (mathematics)

The set of numbers which locate a point in space with respect to a collection of mutually perpendicular axes.

## Cartesian coordinates

(mathematics, graphics)(After Renee Descartes, French
philosopher and mathematician) A pair of numbers, (x, y),
defining the position of a point in a two-dimensional space by
its perpendicular projection onto two axes which are at right
angles to each other. x and y are also known as the
abscissa and ordinate.

The idea can be generalised to any number of independent axes.

Compare polar coordinates.

The idea can be generalised to any number of independent axes.

Compare polar coordinates.