diagonála

Diagonála is a term used in geometry to describe a line segment connecting two non-adjacent vertices of a polygon or polyhedron. In a polygon, a diagonal connects two vertices that do not share an edge. For example, a square has two diagonals, connecting opposite corners. A pentagon has five diagonals, and a hexagon has nine. The number of diagonals in a polygon with n sides can be calculated using the formula n(n-3)/2.

In three-dimensional objects like polyhedra, a diagonal can be either a face diagonal or a space diagonal. A face diagonal connects two non-adjacent vertices on the same face of the polyhedron. A space diagonal, on the other hand, connects two vertices that do not lie on the same face. A cube, for instance, has face diagonals on each of its six square faces and four space diagonals connecting opposite corners through the interior of the cube. The concept of a diagonal is fundamental in understanding the structure and properties of geometric shapes.