coordinat

A coordinat is an ordered set of numbers that locates a point in a space relative to a chosen coordinate system. The numbers are called coordinates, and together they determine the point’s position within that space. The same point can have different coordinates depending on the coordinate system, since the origin and axes define how positions are measured.

Common coordinate systems include Cartesian (rectangular), polar, cylindrical, and spherical. In two-dimensional Cartesian coordinates a point is written as (x, y). In polar coordinates it is (r, θ), with x = r cos θ and y = r sin θ. In three dimensions, Cartesian coordinates are (x, y, z); cylindrical coordinates are (r, φ, z); and spherical coordinates are (ρ, φ, θ), with various conventions for the angle notation. More generally, coordinates are the values of coordinate functions that assign a number to each point in the space.

Coordinate transformations change the representation of a point without changing its geometric location. Examples include translations, rotations, and scalings that re-express the same point in a different coordinate system. Such transformations form the basis of coordinate geometry and are essential in applications that require switching between descriptive frameworks.

Coordinats are fundamental in numerous fields, including geometry, physics, computer graphics, geographic information systems (GIS), robotics, and data analysis, where positions must be described, compared, and manipulated consistently.

See also coordinate system, coordinate geometry, coordinate transformation, and homogeneous coordinates.