Monikulmioissa

Monikulmioissa (Finnish for "in the polygons" or "within polygons") is a descriptive term used in geometry to refer to properties, constructions and problems that arise inside polygonal figures. It encompasses basic definitions, measurements and techniques applied to polygons of any number of sides.

A polygon is a closed planar figure formed by a finite sequence of straight line segments. Polygons are classified as simple (non-self-intersecting) or complex (self-intersecting), and as convex or concave. Regular polygons have all sides and interior angles equal. Key formulas that appear in discussions of monikulmioissa include the interior angle sum (n − 2) × 180° for an n-sided polygon, the constant exterior angle sum of 360°, and the number of diagonals n(n − 3)/2.

Topics treated within polygons include area computation—via triangulation, coordinate methods, or special results such as Pick’s theorem for lattice polygons—perimeter, centroid and moment calculations, and partitioning into simpler components. Triangulation and ear-clipping are common algorithmic approaches for processing polygonal regions in computational geometry. Applications span computer graphics, geographic information systems, architectural design and tiling theory, where polygonal subdivisions and symmetry considerations are central.

Monikulmioissa also covers problems of polygonal inequalities, self-intersection detection, and combinatorial enumeration of polygonal types. The study integrates elementary Euclidean geometry with algebraic and algorithmic methods, forming a foundational part of both theoretical and applied planar geometry.