polügoone

Polügoone is the Estonian term for a polygon, a plane figure formed by straight sides. A polygon is defined by a finite sequence of line segments connected end to end in a closed chain; the segments are the sides and their endpoints are the vertices. The number of sides is called n, with n at least 3.

A polygon can be simple or complex. A simple polygon does not cross itself, while a complex (self-intersecting) polygon may form star-like shapes. In common geometry, convex polygons have all interior angles less than 180 degrees and any line segment between two points inside stays inside; concave polygons have at least one interior angle greater than 180 degrees and at least one diagonal that lies outside the polygon.

Regular polygons are polygons with all sides and all angles equal. The interior angle sum of a simple polygon with n sides is (n−2)×180 degrees, and the exterior angle sum is 360 degrees. The number of diagonals in a polygon is n(n−3)/2.

Perimeter is the sum of the lengths of the sides. The area of a general polygon can be computed by the shoelace formula if the vertices are known in order; for a regular polygon with side length s and n sides, the area is A = (n s^2) / (4 tan(π/n)).

Polügoon concepts appear across mathematics, computer graphics (as polygon meshes), cartography and GIS for map representations, architecture and tiling. The term derives from Greek poly, many, and gonia, angle, and is used in Estonian mathematical terminology to denote polygon.