diagonal

Definitions

  • Diagonal Scale
    Diagonal Scale
  • WordNet 3.6
    • adj diagonal having an oblique or slanted direction
    • adj diagonal connecting two nonadjacent corners of a plane figure or any two corners of a solid that are not in the same face "a diagonal line across the page"
    • n diagonal a punctuation mark (/) used to separate related items of information
    • n diagonal (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
    • n diagonal an oblique line of squares of the same color on a checkerboard "the bishop moves on the diagonals"
    • n diagonal a line or cut across a fabric that is not at right angles to a side of the fabric
    • n diagonal (geometry) a straight line connecting any two vertices of a polygon that are not adjacent
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Webster's Revised Unabridged Dictionary
  • Interesting fact: The king crab walks diagonally.
    • Diagonal A diagonal cloth; a kind of cloth having diagonal stripes, ridges, or welts made in the weaving.
    • Diagonal (Engin) A member, in a framed structure, running obliquely across a panel.
    • Diagonal A right line drawn from one angle to another not adjacent, of a figure of four or more sides, and dividing it into two parts.
    • a Diagonal (Geom) Joining two not adjacent angles of a quadrilateral or multilateral figure; running across from corner to corner; crossing at an angle with one of the sides.
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Century Dictionary and Cyclopedia
    • diagonal In geometry, extending, as a line, from one angle to another not adjacent, within any figure.
    • diagonal Being in an oblique direction; lying obliquely.
    • diagonal Marked by oblique lines: as, diagonal cloth.
    • diagonal A soft material used as a ground for embroidery, generally made very wide, and dyed in plain colors without pattern.
    • diagonal A material for men's wear, especially for coats and waistcoats.
    • n diagonal A straight line drawn from one angle to or through another, not adjacent, in any plane or solid figure.
    • n diagonal Any oblique line.
    • n diagonal Specifically.
    • n diagonal In chess, checkers, etc., a line of squares running diagonally across the board. See chess.
    • n diagonal Same as diagonal cloth, especially in the United States: a term introduced about 1875.
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Chambers's Twentieth Century Dictionary
    • adj Diagonal dī-ag′o-nal through the corners, or from an angle to an opposite angle of a four or many sided figure
    • n Diagonal a straight line so drawn
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Quotations

  • William R. Alger
    William R. Alger
    “The line of life is a ragged diagonal between duty and desire.”

Etymology

Webster's Revised Unabridged Dictionary
L. diagonalis, fr. Gr. from to angle; dia` through + an angle; perh. akin to E. knee,: cf. F. diagonal,

Usage

In literature:

They are so folded that they are about 3 inches wide and as long as the diagonal of the fabric.
"The Seminole Indians of Florida" by Clay MacCauley
They crossed the court diagonally and entered a house in the right-hand corner.
"The Mummy and Miss Nitocris" by George Griffith
Steadily, on a slightly diagonal line, it moved up the British slope.
"Deeds that Won the Empire" by W. H. Fitchett
He decided to pull diagonally across the current towards shore, the mere sight of which would be reassuring.
"Raftmates" by Kirk Munroe
DIAGONALS: Sharpens and transmits.
"St. Nicholas Magazine for Boys and Girls, Vol. 5, January 1878, No. 3" by Various
You could move the gun diagonally in any direction in one motion, but you had to push or pull the opposite way.
"Four-Day Planet" by Henry Beam Piper
There are buttresses set diagonally at the two northern angles of the porch.
"Bell's Cathedrals: Wimborne Minster and Christchurch Priory" by Thomas Perkins
Press the butt down quickly and throw the gun diagonally across the body, to the position shown here.
"The Plattsburg Manual" by O.O. Ellis and E.B. Garey
She was running diagonally across the lawn, trying to intercept the car.
"The Outdoor Girls in a Motor Car" by Laura Lee Hope
Diagonally opposite is the Metropolitan Hotel, in the rear of which is the theatre known as Niblo's Garden.
"Lights and Shadows of New York Life" by James D. McCabe
The pillars are strengthened against lateral yielding by horizontal and diagonal bracing.
"Encyclopaedia Britannica, 11th Edition, Volume 4, Part 3" by Various
From the Ohio mounds also there are examples of plain as well as of diagonal interlacing.
"Prehistoric Textile Art of Eastern United States" by William Henry Holmes
The black square of the window had turned to gray; arrows of rain shot diagonally across it.
"Quin" by Alice Hegan Rice
It was a huge shark, which advanced diagonally toward him, his terrible jaws open wide.
"The Wizard of the Sea" by Roy Rockwood
The figures marked on the diagonal line indicate the boiler efficiency.
"Engineering Bulletin No 1: Boiler and Furnace Testing" by Rufus T. Strohm
It is easy to put all these parallels, perpendiculars, and diagonals into perspective, and then to draw the hexagons.
"The Theory and Practice of Perspective" by George Adolphus Storey
The jump was diagonal, and made under most difficult circumstances.
"Two Boys in Wyoming" by Edward S. Ellis
The cloud passed across the straits diagonally to the south-west.
"Left on Labrador" by Charles Asbury Stephens
Thereupon I backed into the diagonal corner, and stood stock still.
"The Black Wolf's Breed" by Harris Dickson
The smoke was ascending towards the sky, diagonally drifting across the blue disc outlined by the rim of rock.
"The Lone Ranche" by Captain Mayne Reid
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In poetry:

The swimmer's torso dilates out diagonally.
Two outstretched arms line up alongside one another.
The swimmer's heart is sheer see-through like a jellyfish,
The swimmer's eyes hears bells ringing,
The swimmer's mind sees the moon above water.
"The Swimmer" by Sakutaro Hagiwara

In news:

Rest the eggplants on a serving platter for a few minutes before slicing them diagonally into serving pieces.
The Firefly portable LED display from Visual Tech Communications is available with 110-and 164-inch diagonal screens.
1 loaf day old Italian Bread - slice diagonally into one inch slices (available in your grocer bakery section).
Place a bamboo skewer through the heart on a diagonal.
The set will measure 84 inches on the diagonal, making the screen area four times as large as 42-inch sets.
This satellite image provided by GeoEye shows the path of a tornado, diagonal from bottom left to upper right, which struck Harrisburg, Ill.
As you've likely heard by now, iPhone 5 sports a larger screen than its predecessors, now measuring 4-inches diagonally.
It's an iPod dock that also has a 50-lumen projector and can project an image up to 10 feet diagonal in 16:9 format.
I cut the pods diagonally into small pieces and sauté.
Cut in half through the middle on the diagonal and repeat with the remaining omelets and filling.
Add a diagonal green line with three smaller lines reaching out on each side.
They're meant to be eaten whole or sliced diagonally in half.
Perfection on the Diagonal.
A diagonal bunker that runs from 245 yards on the right side out to 290 yards near the center of the fairway will gobble up a less-than- perfect drive and threatens to turn a birdie into a bogey should your reach exceed your grasp.
2 Stamp Grid Paper Backgrounder diagonally on tag and pierce at intersection of each line.
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In science:

Here, Λ is a diagonal matrix with real diagonal matrix elements λk ≥ 0.
Random Matrix Theory and Chiral Symmetry in QCD
The simplest model for D is obtained by replacing the diagonal matrix with positive Matsubara frequencies by the identity matrix times an effective Matsubara frequency t, and replacing the diagonal matrix with negative Matsubara frequencies by the opposite effective Matsubara frequency.
Random Matrix Theory and Chiral Symmetry in QCD
C is a diagonal matrix with Ckk = t − iµ for one half of the diagonal elements and Ckk = −t − iµ for the other half.
Random Matrix Theory and Chiral Symmetry in QCD
In these models, the elements of Y (n) that are above the diagonal are complex (0, 1/n)–Gaussian random variables, and we show that a number of different choices are possible for the diagonal entries.
Invariant subspaces of Voiculescu's circular operator
In §3, we consider upper triangular random matrices whose entries strictly above the diagonal are i.i.d. complex Gaussian random variables which are independent of the diagonal entries.
Invariant subspaces of Voiculescu's circular operator
In §4, we generalize asymptotic freeness results which Voiculescu originally proved for Gaussian random matrices and constant diagonal matrices; we allow the diagonal matrices to be random, sub ject to certain conditions.
Invariant subspaces of Voiculescu's circular operator
Now, on the one hand, the diagonal matrix ∆β := (cid:16) β 0 0 β ∗ (cid:17) commutes with C +AC β eB∆β is real and positive in and, on the other hand, the secondary diagonal in ∆+ the upper right corner, thus, in particular, nonzero.
On the Gribov Problem for Generalized Connections
The random Laplacian matrix L of size N is defined as L = D − M where M is a random incidence matrix (see Sec. 2) with vanishing diagonal elements and D is the diagonal matrix whose element Dii = Pj 6=i Mij is the connectivity of the vertex i in the random graph associated to M .
Random incidence matrices: moments of the spectral density
N ) where γk are linear combinations of the random coefficients x. α and β are the off-diagonal and diagonal matrix elements, respectively.
Two-Body Random Ensembles: From Nuclear Spectra to Random Polynomials
This means that (possibly after stabilization) it is a product of elementary matrices and diagonal matrices with group elements on the diagonal.
Dual 2-complexes in 4-manifolds
This means that after stabilization it is a product of a diagonal matrix with group elements on the diagonal, and elementary matrices.
Dual 2-complexes in 4-manifolds
This Hamiltonian has diagonal disorder, and one expects to find all the eigenfunctions localized; however, for small E , the diagonal terms can be ignored for lengths such that E e2β << 1.
Breakdown of Conformal Invariance at Strongly Random Critical Points
The diagonal operator ∆ is random, and its diagonal entries ∆(j ) can be easily described.
Coordinate restrictions of linear operators in $l_2^n$
The terms beneath the diagonal have extra powers of N for a fixed power of v and would therefore dominate the diagonal terms in a fixed-r, large N limit.
M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
It was argued by Paban, Sethi, and Stern (1998a, 1998b) that there can be no (below-diagonal) higher-loop corrections to the v4 and v6 terms on the diagonal.
M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory
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