coordonnées

Coordonnées is a term used in mathematics, geography and related fields to denote numerical values assigned to a point relative to a chosen reference frame. They specify the position of a point within a coordinated space by a ordered list of numbers.

In mathematical contexts, a point in an n-dimensional space is represented by an n-tuple of coordinates. In a Cartesian system, coordinates correspond to distances along orthogonal axes, with the origin serving as the reference point. The order of the coordinates matters, and changing the basis or applying transformations such as translation, rotation or scaling alters their numeric values while preserving the underlying point. Distances between points are computed from their coordinates using appropriate formulas, such as the Euclidean distance in standard Cartesian space.

Common coordinate systems include Cartesian (rectangular) coordinates, polar coordinates (r, θ) in two dimensions, and their extensions in three dimensions: cylindrical coordinates (r, θ, z) and spherical coordinates (ρ, φ, θ). Each system provides a different way to express the same point, with conversion formulas linking the systems.

Geographic coordinates describe positions on the Earth’s surface using latitude and longitude, often complemented by altitude. They are typically expressed in degrees, minutes and seconds or in decimal degrees. Geographic coordinate systems rely on a reference ellipsoid (datum) such as WGS84 and can be related through map projections and datum transformations. These concepts are fundamental in cartography, navigation, GIS and geospatial analysis.

Coordinate concepts also underpin computer graphics, robotics and data science, where points are represented in coordinate spaces and manipulated through linear algebra and geometry.