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Cartesian coordinates

Cartesian coordinates (kärtē´zhən) [for René Descartes], 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.

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Cartesian projection

Cartesian projection A mapping technique in which every plane in the area being mapped is projected on to a plane in the map and every line on to a line. Each point in the area under study is identified by three values, representing its location in relation to three mutually perpendicular axes (the Cartesian coordinates of the point). These coordinates are transformed mathematically into a homogeneous set of four coordinates which can then be plotted to produce a graphic representation (a map). The word ‘Cartesian’ is derived from the name of the French mathematician René Descartes (1596–1650).

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Cartesian projection

Cartesian projection A technique for the mapping of space in which every plane in the area being mapped is projected on to a plane in the map and every line on to a line. Each point in the area under study is identified by three values, representing its location in relation to three mutually perpendicular axes (the Cartesian coordinates of the point). These coordinates are transformed mathematically into a homogeneous set of four coordinates which can then be plotted to produce a graphic representation (a map). The word ‘Cartesian’ is derived from the name of René Descartes (1596–1650).

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Cartesian coordinates

Cartesian coordinates System in which the position of a point is specified by its distances from intersecting lines (axes). In the simplest type – rectangular coordinates in two dimensions – two axes are used at right angles: x and y. The position of a point is then given by a pair of numbers (x, y). The abscissa, x, is the point's distance from the y axis, measured in the direction of the x axis, and the ordinate, y, is the distance from the x axis. The axes in such a system need not be at right angles but should not be parallel to each other. Three axes represent three dimensions.

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Cartesian

Cartesian of or relating to the ideas of the philosopher René Descartes (1596–1650), deriving from Cartesius, the Latinized form of his name.
Cartesian coordinates numbers which indicate the location of a point relative to a fixed reference point (the origin), being its shortest (perpendicular) distances from two fixed axes (or three planes defined by three fixed axes) which intersect at right angles at the origin.

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Cartesian coordinates

Car·te·sian co·or·di·nates • pl. n. Math. numbers that indicate the location of a point relative to a fixed reference point (the origin), being its shortest (perpendicular) distances from two fixed axes (or three planes defined by three fixed axes) that intersect at right angles at the origin.

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Cartesian

Car·te·sian / kärˈtēzhən/ • adj. of or relating to Descartes and his ideas. • n. a follower of Descartes. DERIVATIVES: Car·te·sian·ism / -ˌnizəm/ n.

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Cartesian

Cartesian XVII. — modL. Cartesiānus, f. Cartesius, latinized form of the surname of René Descartes, French philosopher and mathematician (1596–1650); see -IAN.

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Cartesian

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