Repere

Repère is a term used in French to denote a marker, reference point, or coordinate frame. In mathematics and related disciplines, a repère serves as a reference against which positions and directions are measured. The noun derives from the verb repérer, meaning to locate or identify.

In geometry and analytic geometry, a repère (or frame of reference) consists of an origin and a set of basis directions that define how coordinates are assigned to points. In the plane, a repère cartésien uses two perpendicular axes meeting at the origin; a point is given by coordinates (x, y). In space, three perpendicular axes yield (x, y, z).

Repères are not fixed objects but can be transformed into other frames through translations, rotations, and, in some contexts, scalings. Observers in physics may describe events relative to different repères; the corresponding coordinates are related by mathematical transformations such as Galilean or Lorentz transformations, depending on the theory.

Outside pure mathematics, repères appear in surveying and navigation as reference points or grids on maps, in robotics and computer graphics as coordinate frames for objects and sensors, and in architecture and urban planning for locating features within a reference system.