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In geometry, a Cartesian coordinate system (UK: / k ɑːr ˈ t iː zj ə n /, US: / k ɑːr ˈ t iː ʒ ə n /) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines ...
Special cases are called the real line R 1, the real coordinate plane R 2, and the real coordinate three-dimensional space R 3. With component-wise addition and scalar multiplication, it is a real vector space. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the ...
Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2,3) in green, (−3,1) in red, (−1.5,−2.5) in blue, and the origin (0,0) in purple. In analytic geometry, the plane is given a coordinate system, by which every point has a pair of real number coordinates.
For example, the coordinate surfaces obtained by holding ρ constant in the spherical coordinate system are the spheres with center at the origin. In three-dimensional space the intersection of two coordinate surfaces is a coordinate curve. In the Cartesian coordinate system we may speak of coordinate planes.
An example is the number line, each point of which is described by a single real number. [1] Any straight line or smooth curve is a one-dimensional space, regardless of the dimension of the ambient space in which the line or curve is embedded. Examples include the circle on a plane, or a parametric space curve.
The most basic example is the flat Euclidean plane, an idealization of a flat surface in physical space such as a sheet of paper or a chalkboard. On the Euclidean plane, any two points can be joined by a unique straight line along which the distance can be measured.
For a geographic coordinate system of the Earth, the fundamental plane is the Equator. Astronomical coordinate systems have varying fundamental planes: [2] The horizontal coordinate system uses the observer's horizon. The Besselian coordinate system uses Earth's terminator (day/night boundary). [3] This is a Cartesian coordinate system (x, y, z).
The Y axis is also in the plane of the equator, passing through extending from 90°W longitude (negative) to 90°E longitude (positive) An example is the NGS data for a brass disk near Donner Summit, in California. Given the dimensions of the ellipsoid, the conversion from lat/lon/height-above-ellipsoid coordinates to X-Y-Z is straightforward ...