Diagonal

For other uses, see Diagonal (disambiguation).

The diagonals of a cube with side length 1. AC' (shown in blue) is a space diagonal with length ${\sqrt {3}}$, while AC (shown in red) is a face diagonal and has length ${\sqrt {2}}$.

Horizontal (left), vertical (center) and diagonal (right) double arrows.

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 corner to corner" (from διά- dia-, "through", "across" and γωνία gonia, "corner", 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").