diagonáln

Diagonáln is a term used in geometry and related disciplines to refer to diagonals, line segments that connect non-consecutive vertices of a polygon or polyhedron. In some languages, including Hungarian, a cognate form is used to describe diagonal concepts, and the word can appear in mathematical texts and design contexts. The term is not widely established as an independent topic in English-language mathematics, where the standard term is diagonal.

In a simple polygon with n vertices, the number of diagonals is n(n-3)/2. Diagonals can intersect inside the polygon; triangulations partition the polygon into triangles by drawing non-crossing diagonals. A diagonal from a given vertex can be counted as n-3.

In polyhedra, diagonals connect non-adjacent vertices; the diagonal set includes face diagonals (on polygonal faces) and space diagonals that pass through the interior of the solid. Counting all diagonals depends on the specific structure and is more complex than in two dimensions.

Diagonals are used in computer graphics for mesh generation and rendering, in architectural design for structural or aesthetic lines, and in mathematics for polygon triangulation and graph theory. The concept also appears in grid-based reasoning and data visualization where diagonals define connections between non-adjacent grid points.

See also diagonal, diagonality, diagonalization, triangulation. Etymology: from Latin diagonalis. In Hungarian usage, diagonál/diagonális forms relate to the same concept.