polygones

Polygons are plane figures bounded by a closed chain of straight line segments called sides, which meet at vertices. A simple polygon has no self-intersections; when no interior angle exceeds 180 degrees, the polygon is convex; if an interior angle is greater than 180 degrees, it is concave. A polygon with n sides is an n-gon, with n ≥ 3.

Key properties: the sum of interior angles is (n−2)×180 degrees; the exterior angles around the figure sum to 360 degrees. The perimeter equals the sum of the side lengths. The area depends on the shape; for a regular n-gon with side length s, A = (n s^2) / (4 tan(π/n)). In general, area can be computed by triangulation or by the shoelace formula.

Classification and examples: triangles and quadrilaterals are common polygons. Regular polygons have all sides and angles equal; star polygons (self-intersecting) extend the concept. In computer graphics and GIS, polygons are used to model surfaces, regions, and boundaries.

Terminology and origin: the term polygon comes from Greek poly- “many” and gonia “angles.” The plural polygones is used in French; in English the preferred plural is polygons.