coordonnees

Coordonnees, or coordinates, are numerical values that specify the position of a point within a given reference frame. In mathematics, a coordinate is an element of an ordered n-tuple that locates a point relative to an origin and a set of axes. In two dimensions, a point is given by (x, y); in three dimensions, by (x, y, z).

Coordinate systems come in several forms. Cartesian coordinates use orthogonal axes; polar coordinates describe a point by a distance from the origin and an angle. Cylindrical coordinates extend polar with a height component, and spherical coordinates describe a point by radius and two angles. Homogeneous coordinates add an extra scale factor to facilitate certain transformations, especially in projective geometry and computer graphics.

Geographic coordinates are used to locate positions on the Earth and typically consist of latitude and longitude, sometimes with altitude. They are expressed in degrees or decimal degrees and are defined with respect to a geodetic datum such as WGS84. In maps and geographic information systems (GIS), coordinate reference systems (CRS) specify how coordinates correspond to real locations and how they are projected onto a plane for representation and analysis.

Operations involving coordonnees include transforming coordinates between systems, computing distances and angles, and projecting curved surfaces onto flat maps. Conversions require specific formulas, such as r = sqrt(x^2 + y^2) and theta = atan2(y, x) for Cartesian to polar.

Representation and conventions matter: coordinates are stored as numbers in vectors or arrays, with defined order, units, and precision. They underpin a wide range of fields, including geometry, navigation, computer graphics, and geospatial analysis.