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.
    See also — Additional definitions below


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").

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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"