coordenadas

Coordenadas, or coordinates, are the numbers that specify the position of a point in a space relative to a reference system. An ordered set of numbers, together with a coordinate system, uniquely identifies a location. In n-dimensional space, a point is represented by an n-tuple of coordinates; the same point can have different coordinates in different systems.

Common coordinate systems include Cartesian coordinates (x, y, z), polar coordinates (r, theta), cylindrical coordinates (r, theta, z) and spherical coordinates (r, theta, phi). In geography, coordinates are latitude, longitude and altitude, typically defined within a datum such as WGS84. Projections convert between curved surfaces and flat maps, altering units and reference frames used to describe positions.

Coordinates enable quantitative operations such as distance and angle measurement, transformations between systems, interpolation, and the representation of geometric and spatial data. They are used across mathematics, physics, computer graphics, navigation and geographic information systems. Units vary: angular measures are commonly degrees or radians; linear measures are meters, kilometers, etc.

Historically, coordinates were introduced by René Descartes to unite algebra with geometry, giving rise to analytic geometry. Today, coordinates underpin positioning technologies such as GPS, CAD, robotics and geospatial analysis, and they remain a fundamental concept in science and engineering.