Monikulmion

Monikulmio, in geometry, is a plane figure bounded by a closed chain of straight-line segments. The segments meet at vertices, forming a finite number of sides, denoted by n (n ≥ 3). The figure is often described as an n-gon, with examples including triangles (n = 3), quadrilaterals (n = 4), and pentagons (n = 5).

Polygons are commonly classified by shape. A polygon is convex if every interior angle is less than 180 degrees and no line segment joining two points of the polygon lies outside it. If at least one interior angle exceeds 180 degrees, the polygon is concave. A polygon is regular when all its sides and all its interior angles are equal. Irregular polygons have sides or angles of differing lengths or measures.

Key measures for polygons include the perimeter and the interior-angle sum. The perimeter is the sum of the lengths of all sides. The sum of interior angles of a simple n-gon is (n − 2) × 180 degrees, and the sum of exterior angles is 360 degrees.

Area calculations depend on the subtype. For a regular polygon with n sides of length s, the area can be expressed as A = (n s^2) / [4 tan(π/n)]. More generally, the area can be found by dividing the polygon into triangles, using coordinate methods such as the shoelace formula, or applying other decomposition techniques.

In Finnish geometry, monikulmio corresponds to the general concept of a polygon. The term encompasses a wide range of shapes used across mathematics, design, and applied sciences.