Cartesian coordinate system

A Cartesian coordinate system is an orthogonal coordinate system. It is named after the Latinized name Descartes the French mathematician René Descartes, who first made public the concept of " Cartesian coordinates". In the two - and three-dimensional space is the coordinate system most commonly used, as can many geometric facts describing vividly and clearly in this.

The coordinate system in two-dimensional space

The two directional axes are mutually orthogonal, ie, intersect at a 90 ° angle. The coordinate lines are straight lines at a constant distance from each other. Judging from the mathematical dexterity, so refers to the horizontal axis as abscissa (from Latin linea abscissa " cut line " ) or right axis. The vertical axis is called y-axis (from Latin linea ordinata " secondary line " ) or vertical axis.

In mathematics and are often the variables used for designating the coordinates, for example, when lines or curves can be described by equations. We also speak of the axis instead of x-axis and the axis instead of the ordinate axis. The - or value of a point is referred to as abscissa and ordinate, respectively. Sometimes abbreviated as the coordinate axes x-axis or y-axis are called (see y-axis and x - axis, or dependent and independent variable).

As a mnemonic can keep in mind that always belong together each of the alphabet standing front and rear standing designations: to abscissa and ordinate. Another mnemonic: The ordinate shows (with positive values) to the top - the abscissa axis must therefore show (with positive values) to the right.

The point where the two axes meet is called the origin or origo (Latin for " origin ").

For a point with the coordinates and to write or even.

Left-handed Cartesian coordinate systems

In geodesy, the coordinate axes are interchanged, also be limited geodetic coordinate systems in order to avoid negative values ​​, sometimes to the first quadrant.

More-than- two-dimensional coordinate system,

In three-dimensional space is still a third axis added, the spatial axis ( axis, not shown here), applicate ( in geography: Kote ) called. Mostly are here - and - axis in the plane, and the axis is used for altitude display. Graphically give points here a point cloud.

And axis reversed, while the - axis shows as well as the mathematical coordinate system to the top - As in the two-dimensional case are also three-dimensional geodetic coordinate systems.

In the generalization of the mathematics sees higher dimensional spaces ( see: 4D ) ago. For example, the axis of the extension in space of the fourth dimension is then sometimes referred to as the axis, the extension directions as ana ( "top" ) and catalytic ( "bottom ").

Exemplary applications

In physics, the right axis is commonly used for displaying the time as an independent variable; of her is then spoken of as the time - and - axis, while the vertical axis of the time-varying size, such as the distance traveled or the speed, and accordingly represented as - is called or axis.

Three-dimensional coordinate systems, for example, allow the display of two-dimensional statistical distribution, in which the height axis indicates the probability density function and.

Your Perhaps the best known application have three-dimensional coordinates today in the navigation, such as the location of an object by means of GPS or as a reference system for describing the spatial orientation of an object using the RPY angle (where the coordinate systems used to apply Cartesian locally only as approximate, in reality, however, spherical coordinate systems ).

History

Apollonius writes in Definition 4 of Konika parallels that are "pulled subservient" to the diameter of a conic section. The Greek term for "ordered", tetagmenos is reproduced as Latin ordinatim. This is the origin of the word " ordinate ".

The first known use of the words abscissa and ordinate is found in a letter from Leibniz to Henry Oldenburg dated August 27 of 1676.