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A diagonal can refer to a line joining two nonconsecutive vertices of a polygon or polyhedron, or in contexts any upward or downward sloping line. The word "diagonal" derives from the Greek διαγώνιος (diagonios), used by both Strabo and Euclid to refer to a line connecting two vertices of a rhombus or cuboid, and is formed from dia- ("through", "across") and gonia ("angle", related to gony "knee."), later adopted into Latin as diagonus ("slanting line").

In mathematics, in addition to its geometric meaning, a diagonal is also used in matrices to refer to a set of entries along a diagonal line.

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.

Any n-sided polygon (n ≥ 3), convex or concave, has

- $frac\{n(n-3)\}\{2\},$

In geometric studies, the idea of intersecting the diagonal with itself is common, not directly, but by perturbing it within an equivalence class. This is related at a deep level with the Euler characteristic and the zeros of vector fields. For example, the circle S^{1} has Betti numbers 1, 1, 0, 0, 0, and therefore Euler characteristic 0. A geometric way of expressing this is to look at the diagonal on the two-torus S^{1}xS^{1} and observe that it can move off itself by the small motion (θ, θ) to (θ, θ + ε). In general, the intersection number of the graph of a function with the diagonal may be computed using homology via the Lefschetz fixed point theorem; the self-intersection of the diagonal is the special case of the identity function.

- Diagonals of a polygon with interactive animation
- Polygon diagonal from MathWorld.
- Diagonal of a matrix from MathWorld.
- Diagonal media from Diagonal.

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Last updated on Friday October 03, 2008 at 17:19:35 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Friday October 03, 2008 at 17:19:35 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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