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The black dot shows the point with coordinates x = 2, y = 3, and z = 4, or (2, 3, 4). A Cartesian coordinate system for a three-dimensional space consists of an ordered triplet of lines (the axes) that go through a common point (the origin), and are pair-wise perpendicular; an orientation for each axis; and a single unit of length for all three ...
A map is a function, as in the association of any of the four colored shapes in X to its color in Y In mathematics , a map or mapping is a function in its general sense. [ 1 ] These terms may have originated as from the process of making a geographical map : mapping the Earth surface to a sheet of paper.
When a coordinate system is chosen in the Euclidean space, this defines coordinates on : the coordinates of a point of are defined as the coordinates of (). The pair formed by a chart and such a coordinate system is called a local coordinate system , coordinate chart , coordinate patch , coordinate map , or local frame .
Cartesian plane with marked points (signed ordered pairs of coordinates). For any point, the abscissa is the first value (x coordinate), and the ordinate is the second value (y coordinate). In mathematics , the abscissa ( / æ b ˈ s ɪ s . ə / ; plural abscissae or abscissas ) and the ordinate are respectively the first and second coordinate ...
A coordinate map is essentially a coordinate system for a subset of a given space with the property that each point has exactly one set of coordinates. More precisely, a coordinate map is a homeomorphism from an open subset of a space X to an open subset of R n. [15] It is often not possible to provide one consistent coordinate system for an ...
Cardinal directions or cardinal points may sometimes be extended to include vertical position (elevation, altitude, depth): north and south, east and west, up and down; or mathematically the six directions of the x-, y-, and z-axes in three-dimensional Cartesian coordinates. Topographic maps include elevation, typically via contour lines.