poligonok

Poligonok are plane figures bounded by a finite sequence of straight line segments that join end to end and form a closed loop. The segments are called edges and the junctions are vertices. The region inside the edges is the interior of the polygon. A polygon is simple if its edges do not cross themselves; if they do, the polygon is self‑intersecting or complex.

Polygons are commonly categorized by shape and structure. Convex polygons have the property that any line segment joining two points of the polygon lies entirely within the polygon, and all interior angles are less than 180 degrees. Concave polygons have at least one interior angle greater than 180 degrees. Regular polygons have all sides of equal length and all interior angles equal. There are many non‑convex and non‑regular polygons, including star polygons formed by intersecting edges.

Key properties include the sum of interior angles and area computations. For a simple polygon with n sides, the sum of interior angles equals (n − 2) × 180 degrees. The exterior angle sum is always 360 degrees. The area can be computed in several ways, such as using the shoelace formula from vertex coordinates, or for a regular polygon with side length s, area = (n s^2) / (4 tan(pi/n)) or area = (1/2) n s a where a is the apothem.

Polygons appear in many contexts, from pure geometry to computer graphics, geographic information systems, and architectural design. They also underpin tessellations and planar partitioning activities. The term polygon derives from Greek roots meaning “many angles.” In Hungarian, poligonok is the plural form used for polygons.