Diagonal

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word diagonal derives from the ancient Greek διαγώνιος diagonios, "from angle to angle" (from διά- dia-, "through", "across" and γωνία gonia, "angle", related to gony "knee"); it was used by both Strabo and Euclid to refer to a line connecting two vertices of a rhombus or cuboid, and later adopted into Latin as diagonus ("slanting line"). In matrix algebra, the diagonal of a square matrix consists of the entries on the line from the top left corner to the bottom right corner. There are also many other non-mathematical uses. In engineering, a diagonal brace is a beam used to brace a rectangular structure (such as scaffolding) to withstand strong forces pushing into it; although called a diagonal, due to practical considerations diagonal braces are often not connected to the corners of the rectangle. Diagonal pliers are wire-cutting pliers defined by the cutting edges of the jaws intersects the joint rivet at an angle or "on a diagonal", hence the name. A diagonal lashing is a type of lashing used to bind spars or poles together applied so that the lashings cross over the poles at an angle. In association football, the diagonal system of control is the method referees and assistant referees use to position themselves in one of the four quadrants of the pitch. As applied to a polygon, a diagonal is a line segment joining any two non-consecutive vertices. Therefore, a quadrilateral has two diagonals, joining opposite pairs of vertices. For any convex polygon, all the diagonals are inside the polygon, but for re-entrant polygons, some diagonals are outside of the polygon. Any n-sided polygon (n ≥ 3), convex or concave, has total diagonals, as each vertex has diagonals to all other vertices except itself and the two adjacent vertices, or n − 3 diagonals, and each diagonal is shared by two vertices.