# What is diagonal?

• (noun): (mathematics) a set of entries in a square matrix running diagonally either from the upper left to lower right entry or running from the upper right to lower left entry.

## Diagonal

A diagonal is a line joining two nonconsecutive vertices of a polygon or polyhedron. 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").

### Some articles on diagonal:

Diagonal - Geometry
... consisting of all pairs (x,x), is called the diagonal, and is the graph of the identity relation ... points of a mapping F from X to itself may be obtained by intersecting the graph of F with the diagonal ... In geometric studies, the idea of intersecting the diagonal with itself is common, not directly, but by perturbing it within an equivalence class ...

### More definitions of "diagonal":

• (noun): An oblique line of squares of the same color on a checkerboard.
Example: "The bishop moves on the diagonals"
• (noun): A line or cut across a fabric that is not at right angles to a side of the fabric.
Synonyms: bias
• (noun): (geometry) a straight line connecting any two vertices of a polygon that are not adjacent.
• (adj): At an angle; especially connecting two nonadjacent corners of a plane figure or any two corners of a solid that are not in the same face.
Example: "A diagonal line across the page"