 A diagonal can refer to a line joining two nonadjacent vertices of a polygon or polyhedron, or in contexts any upward or downward sloping line. The word "diagonal" was originally from the Greek διαγωνιος (diagonios), used by both Strabo[1] and Euclid[2] to refer to a line connecting two vertices of a rhombus or cuboid,[3] and is formed from dia- ("through", "across") and gonia ("angle", related to gony "knee."), later adopted into Latin as diagonus ("slanting line"). Image File history File links Size of this preview: 577 × 600 pixelsFull resolution (1856 × 1929 pixel, file size: 118 KB, MIME type: image/jpeg) Autor: ErvÃn PospÃÅ¡il File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Diagonal...
Look up polygon in Wiktionary, the free dictionary. ...
A polyhedron (plural polyhedra or polyhedrons) is a geometric object with flat faces and straight edges. ...
For other uses of the word rhombus, see Rhombus (disambiguation) This shape is a rhombus In geometry, a rhombus (or rhomb; plural rhombi) is a quadrilateral in which all of the sides are of equal length, i. ...
In anatomy, the cuboid bone is a bone in the foot. ...
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. Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...
For the square matrix section, see square matrix. ...
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. Engineering is the design, analysis, and/or construction of works for practical purposes. ...
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. Diagonal pliers. ...
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. The diagonal lashing is a type of lashing. ...
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. The striker (wearing red jersey) has run past the defender (in white jersey) and is about to take a shot at the goal, while the goalkeeper positions himself to stop the ball. ...
In association football, the diagonal system of control is the method referees and assistant referees use to position themselves. ...
Polygons 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. Look up polygon in Wiktionary, the free dictionary. ...
The geometric definition of a line segment In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. ...
In geometry, a quadrilateral is a polygon with four sides and four vertices. ...
A convex pentagon In geometry, a convex polygon is a simple polygon whose interior is a convex set. ...
A re-entrant, or concave polygon is one in which at least one interior angle is more than 180 degrees (i. ...
Any n-gon (an n-sided polygon), convex, or concave, has Look up convex in Wiktionary, the free dictionary. ...
Look up Concave in Wiktionary, the free dictionary. ...
 diagonals, as each vertex has diagonals to all other vertices except itself and the two adjacent vertices, or n − 3 diagonals.
Matrices In the case of a square matrix, the main or principal diagonal is the diagonal line of entries running from the top-left to bottom-right corners. For example, the identity matrix can be defined as having entries of 1 on the main diagonal, and 0s elsewhere. The top-right to bottom-left diagonal is sometimes described as the minor diagonal or antidiagonal. A superdiagonal entry is one that is above and to the right of the main diagonal. If otherwise unqualified, it refers to the one adjacent to the main diagonal. Likewise, a subdiagonal entry is one that is directly below and to the left of the main diagonal. A diagonal matrix is one whose off-diagonal entries are all zero. For the square matrix section, see square matrix. ...
In linear algebra, the identity matrix of size n is the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. ...
Geometry By analogy, the subset of the Cartesian product X×X of any set X with itself, consisting of all pairs (x,x), is called the diagonal, and is the graph of the identity relation. This plays an important part in geometry; for example, the fixed points of a mapping F from X to itself may be obtained by intersecting the graph of F with the diagonal. A is a subset of B, and B is a superset of A. In mathematics, especially in set theory, the terms, subset, superset and proper (or strict) subset or superset are used to describe the relation, called inclusion, of one set being contained inside another set. ...
In mathematics, the Cartesian product is a direct product of sets. ...
In mathematics, a fixed point (sometimes shortened to fixpoint) of a function is a point that is mapped to itself by the function. ...
Partial plot of a function f. ...
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 S1 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 S1xS1 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. In mathematics, given a set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a: [a] = { x ∈ X | x ~ a } The notion of equivalence classes is useful for constructing sets out...
It has been suggested that Vertex/Face/Edge relation in a convex polyhedron be merged into this article or section. ...
Vector field given by vectors of the form (-y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a Euclidean space. ...
Circle illustration This article is about the shape and mathematical concept of circle. ...
In algebraic topology, the Betti number of a topological space is, in intuitive terms, a way of counting the maximum number of cuts that can be made without dividing the space into two pieces. ...
In geometry, a torus (pl. ...
In mathematics, the Lefschetz fixed-point theorem counts the number of fixed points of a mapping from a topological space X to itself (subject to some mild conditions on X), by means of traces of the induced mappings on the homology groups of X. The counting is subject to some...
See also In linear algebra, a diagonal matrix is a square matrix in which the entries outside the main diagonal are all zero. ...
In linear algebra, the Jordan normal form, also called the Jordan canonical form, named in honor of the 19th and early 20th-century French mathematician Camille Jordan, answers the question, for a given square matrix M over a field K containing the eigenvalues of M, to what extent can M...
In linear algebra, the main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. ...
In category theory, for any object a in any category C where the product a×a exists, there exists the diagonal morphism δa: a → a×a, satisfying πkδa = ida for k=1,2, where πk is the canonical projection morphism to the k-th component. ...
BD is a face diagonal while AC is a space diagonal In geometry, a face diagonal of a polyhedron is a diagonal on one of the faces, in contrast to a space diagonal passing through the interior of the polyhedron. ...
In a magic cube, the four space diagonals are the lines that go from a corner of the cube, through the center of the cube , to the opposite corner. ...
External links Look up diagonal in Wiktionary, the free dictionary. Wikipedia does not have an article with this exact name. ...
Wiktionary (from wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ...
MathWorld is an online mathematics reference work, sponsored by Wolfram Research Inc. ...
MathWorld is an online mathematics reference work, sponsored by Wolfram Research Inc. ...
References - ^ Strabo, Geography 2.1.36-37
- ^ Euclid, Elements book 11, proposition 28
- ^ Euclid, Elements book 11, proposition 38
|
Feeds |
Contact