planeaariset

Planeaariset is a Finnish term used in mathematics to describe properties and objects that lie in or can be represented in a plane. In geometry, planeaariset objects are those whose points can all be contained in a single two-dimensional plane. In graph theory, a graph is planeaarinen or planar if it can be drawn on the plane so that its edges intersect only at their endpoints. If such a drawing is impossible, the graph is non-planar. Classic non-planar graphs include the complete graph on five vertices, K5, and the complete bipartite graph K3,3.

Planar objects include common shapes such as triangles, squares and pentagons, as well as many graphs and decompositions that admit a crossing-free embedding in the plane. Planarity is an important constraint in fields like computer graphics, geographic information systems, and electrical circuit design, where planar representations simplify visualization and computation.

Historically, the concept of planarity has been central to graph theory since Euler’s formula for planar graphs and was extended by Kuratowski's theorem to characterize planar graphs. In Finnish mathematical writing, planeaariset is used alongside terms like tasogeometria (plane geometry) and graafiteoria (graph theory) to denote planarity-related ideas.

See also: planar graphs, plane geometry, Euler characteristic, Kuratowski’s theorem.