diagonaaliset

Diagonaaliset is a Finnish term that refers to diagonals, the straight-line segments that connect two non-adjacent vertices in polygons, polyhedra, and certain mathematical structures such as matrices. The concept is a common element in geometry, linear algebra, and design, and its interpretation varies with context.

In geometry, a diagonal of a polygon is a segment joining two vertices that are not next to each other and, in a simple polygon, lies inside the figure. For convex polygons all such segments are inside, while in concave polygons some potential diagonals may lie outside. The number of diagonals in an n-sided polygon is n(n−3)/2; for example, a pentagon has five diagonals and a hexagon has nine. Diagonals reveal properties such as symmetry and can be used in triangulation, where a polygon is divided into triangles.

In linear algebra and matrix theory, the term diagonal refers to elements aii that form the main diagonal, and to lines parallel to it, such as the superdiagonal and subdiagonal. Diagonal elements often influence matrix properties, including determinants, eigenvalues, and matrix powers, and they appear in algorithms for solving systems of equations and for performing certain types of decompositions.

Diagonaaliset also appear in applied fields like computer graphics, tiling, architecture, and game design, where diagonal lines and patterns contribute to structure, perspective, or visual rhythm. The concept remains a foundational building block across disciplines.