Cartesian coordinates


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Cartesian coordinates

(kärtē`zhən) [for René DescartesDescartes, 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.
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], 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 geometryanalytic 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.
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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.
References in periodicals archive ?
In the current application of the membrane elements, a traditional manner has been adopted to establish the local Cartesian coordinate system over an element [5].
We elected the segment of the line L [equivalent to] {y = x} and when substituting it into the system in cartesian coordinates (6) we obtain
On the basis of data recorded during this flight, the following system measurement errors concerning the obstacle were estimated: the helicopter -to-obstacle distance, the obstacle's position in the Cartesian coordinates, and the relative speed of the obstacle towards the helicopter.
We propagated the dynamics of XHY by solving Newton's equations of motion for each set of initial positions and momenta of the X, H, and Y atoms in Cartesian coordinates,
max] is the radius of the maximum inscribed circle of the original image in Cartesian Coordinates.
Kinematics of the masticatory muscles can be analyzed when taken into account Cartesian coordinates defining the location of insertion of the jaw muscles and bones of the skull.
Our aim here is to establish the exact formulas for the multipole expansion of a source in Cartesian coordinates, which, as far as we know, were not written anywhere.
By tying these abstract concepts to real manufacturing applications, the teaching of Cartesian coordinates and G & M Code can help students develop mathematical and visualization skills that might not otherwise be possible.
the matrix M([theta]', [PHI]') performs a transformation from local spherical coordinates to cartesian coordinates, before rotation, with:
The Cartesian coordinates (X, Y) of the transition curves are calculated via using Fresnel integral (Jeffrey, Dai 2008).
and since the required distance can be found from the Cartesian coordinates of A and B, we should turn students' attention to the task of converting latitude-longitude coordinates into Cartesian ones after informing them that the origin of the Cartesian coordinate system is at the centre of the Earth, the positive part of the x-axis goes through latitude 0 and longitude 0, and the positive part of the z-axis goes through the North Pole.