carrées

Carrées is the plural form of a French noun referring to squares, the geometric shape known in English as a square. In geometry, a carré (square) is a regular quadrilateral with four equal sides and four right angles. It is a special case of both a rectangle (opposite sides are parallel and equal) and a rhombus (all sides equal).

In the Euclidean plane, a carré of side length s has area A = s^2 and perimeter P = 4s. The diagonals have length d = s√2 and intersect at right angles, bisecting each other. A carré can be oriented with its sides parallel to a reference axis or rotated; when rotated by 45 degrees it can appear as a diamond shape.

Beyond pure geometry, carrées are fundamental in tiling, design, and digital imagery. A grid of squares covers the plane in a square tessellation, and digital images are composed of square pixels. The term also appears in number theory in the phrase nombres carrés, which denotes square numbers obtained by squaring integers (e.g., 1, 4, 9, 16).

Etymology and usage: the term carré comes from Latin quadratus via Old French carré; the feminine plural carrées is used when referring to multiple squares or, in some contexts, to feminine formulations in French. In mathematics and education, carrées serve as a standard reference shape for measurements, coordinate geometry, and visual representations of area and symmetry.

See also: square (geometry), rectangle, rhombus, square number, tiling, unit square.