Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Diagonal |
DiagonalAdjective1. 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; "a diagonal line across the page". 2. Having an oblique or slanted direction. Noun1. (geometry) a straight line connecting any two vertices of a polygon that are not adjacent. 2. A line or cut across a fabric that is not at right angles to a side. 3. An oblique line of squares of the same color on a checkerboard; "the bishop moves on the diagonals". 4. (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. 5. A punctuation mark (/) used to separate related items of information. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "diagonal" was first used in popular English literature: sometime before 1380. (references) |
| Domain | Definition |
Industry | Coth that shows an oblique twill line that may run to the left or right on the face of the material. . Source: European Union. (references) |
Source: compiled by the editor from various references; see credits. | |
(From Wikipedia, the free Encyclopedia)
In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology.As applied to a polygon, a diagonal is a line segment joining two vertices that are not adjacent. Therefore a quadrilateral has two diagonals, joining opposite pairs of vertices. For a convex polygon the diagonals run inside the polygon - but not otherwise, for re-entrant polygons. In fact a polygon is convex if and only if the diagonals are internal.
In the case of a square matrix, the main or principal diagonal is the diagonal line of entries running north-west to south-east. For example the identity matrix can be described as having entries 1 on main diagonal, and 0 elsewhere. The north-east to south-west diagonal is sometimes described as the minor diagonal.
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. It is the graph of the identity relation. It 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.
Quite a major role is played in geometric studies by the idea of intersecting the diagonal with itself: not directly, but by passing within an equivalence class. This is related at quite a deep level with the Euler characteristic and the zeroes of vector fields. For example the circle S1 has Betti numbers 1, 1, 0, 0, 0, ... and so Euler characteristic 0. A geometric way of saying that is to look at the diagonal on the two-torus S1xS1; and to observe that it can move off itself by the small motion (θ, θ) to (θ, θ+ε).
See also
- diagonal matrix
- main diagonal
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Diagonal."
(From Wikipedia, the free Encyclopedia)
Diagonal is a city located in Ringgold County, Iowa. As of the 2000 census, the city had a total population of 312.Geography
Diagonal is located at 40°48'32" North, 94°20'29" West (40.808819, -94.341510)1. According to the United States Census Bureau, the city has a total area of 2.4 km² (0.9 mi²). 2.4 km² (0.9 mi²) of it is land and none of it is covered by water.Demographics
As of the census of 2000, there are 312 people, 139 households, and 87 families residing in the city. The population density is 132.4/km² (343.5/mi²). There are 154 housing units at an average density of 65.3/km² (169.6/mi²). The racial makeup of the city is 100.00% White, 0.00% African American, 0.00% Native American, 0.00% Asian, 0.00% Pacific Islander, 0.00% from other races, and 0.00% from two or more races. 0.00% of the population are Hispanic or Latino of any race. There are 139 households out of which 23.0% have children under the age of 18 living with them, 54.0% are married couples living together, 5.8% have a female householder with no husband present, and 36.7% are non-families. 31.7% of all households are made up of individuals and 16.5% have someone living alone who is 65 years of age or older. The average household size is 2.24 and the average family size is 2.85. In the city the population is spread out with 21.2% under the age of 18, 10.9% from 18 to 24, 25.3% from 25 to 44, 24.4% from 45 to 64, and 18.3% who are 65 years of age or older. The median age is 40 years. For every 100 females there are 92.6 males. For every 100 females age 18 and over, there are 87.8 males. The median income for a household in the city is $24,063, and the median income for a family is $28,393. Males have a median income of $22,083 versus $18,958 for females. The per capita income for the city is $16,601. 15.8% of the population and 16.5% of families are below the poverty line. Out of the total people living in poverty, 23.7% are under the age of 18 and 13.3% are 65 or older.Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Diagonal, Iowa."
Synonyms: DiagonalSynonyms: aslant (adj), aslope (adj), slanted (adj), slanting (adj), sloped (adj), sloping (adj), bias (n), separatrix (n), slash (n), solidus (n), stroke (n), virgule (n). (additional references) |
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Source: compiled by the editor from various references; see credits. | |||
| Thumbnail | Description & Credit | Thumbnail | Description & Credit |
 | From an overhead angle, a slice of watermelon, scattered grapes and popcorn kernels are shown on a yellow and black plaid tabletop. Diagonal black letters read: "Choose Low-fat Snacks". Shot on 4x5 format. This was used in the 1989 calendar "Eat for Good Health" September 1989. See artwork: PV-19. Credit: Bill Branson (photographer). |  | Diagonal view of orchestra, proscenium and stage, curtains open. Copy of 1928 photo of completed theater interior, by Canfield and Shook, photographers, courtesy of Drew Eberson, Stamford, Connecticut. (Reproduction Number: HABS, KY,56-LOUVI,17-47) Going to the movies became quite an event in the 1920s. Large, urban motion picture "palaces" originally incorporated all the amenities found in live theaters, even out-doing them in scale and opulence and adding concert hall features such as great electric pipe organs and elaborately decorated lobbies. The Loew's Theatre chain hired nationally-known theater architect John Eberson, who designed this 1928 theater in a Spanish influenced style called Churrigueresque. Credit: Library of Congress. |
 | House of Lawrence Furbura, a Bohemian farmer near Diagonal, Iowa. He rents the farm from his father. There is a Bohemian colony in this vicinity which is inhabited by the most prosperous farmers in Ringgold County, Iowa. Credit: Library of Congress. |  | Everglades Club, Orange Room, Palm Beach, Florida. Diagonal view to stage. Credit: Library of Congress. |
 | National Archives. Dark background with two white diagonal lines intersecting in middle. Credit: Library of Congress. | ||
Source: pictures compiled by the editor from various references; see picture credits. | |||
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| "Powerlines" by Tommy Johansen Commentary: "I nice composition of diagonal lines under a cloudy sky." |
Source: photographs selected by the editor, with permission from the photographers. |
| Subject | Topic | Quote |
Economic History | Burundi | Flag: White diagonal cross with two red and two green panels; white circle in center with three red stars. (references) |
Lesotho | Flag: Diagonal fields of green and blue with a traditional Basotho shield in brown on a diagonal field of white occupying remaining half of flag. (references) | |
Source: compiled by the editor from ICON Group International, Inc.; see credits. | ||
| "Diagonal" is generally used as an adjective (general or positive) -- approximately 99.05% of the time. "Diagonal" is used about 420 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted) |
| Parts of Speech | Percent | Usage per 100 Million Words | Rank in English |
| Adjective (general or positive) | 99.05% | 416 | 13,620 |
| Noun (proper) | 0.95% | 4 | 175,879 |
| Total | 100.00% | 420 | N/A |
Source: compiled by the editor from several corpora; see credits.
| Country | Name |
| United Kingdom | DIAGONAL PLC |
| (more examples...) |
Source: compiled by the editor from Icon Group International, Inc.
1. Diagonal, IA (city, FIPS 21270) |
Expressions using "diagonal": bearish diagonal call spread ♦ bearish diagonal put spread ♦ bearish diagonal spread ♦ bullish diagonal call spread ♦ bullish diagonal put spread ♦ bullish diagonal spread ♦ Diagonal Band of Broca ♦ diagonal bear spread ♦ Diagonal bond ♦ diagonal brace ♦ Diagonal built ♦ diagonal bull spread ♦ Diagonal cleavage ♦ diagonal expansion ♦ diagonal line ♦ diagonal matrix ♦ Diagonal molding ♦ diagonal opera glass ♦ diagonal or side opera glass ♦ diagonal resolution ♦ Diagonal rib ♦ Diagonal scale ♦ Diagonal stratification ♦ main diagonal ♦ principal diagonal ♦ secondary diagonal. Additional references. | |
| Hypenated Usage | |
Ending with "diagonal": counter-diagonal, off-diagonal. | |
| Source: compiled by the editor from various references; see credits. | |
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Expression | Frequency per Day | Expression | Frequency per Day |
diagonal | 39 | diagonal cutter | 3 |
diagonal iowa | 9 | argument category diagonal theory | 3 |
diagonal line | 5 | 2 celestron diagonal inverted | 2 |
cinesa diagonal | 4 | diagonal pattern | 2 |
diagonal of a square | 4 | diagonal formula square | 2 |
diagonal mar | 4 | diagonal polygon | 2 |
2 diagonal erect image | 4 | diagonal television | 2 |
diagonal rectangle | 3 | 13 aquos diagonal flat inch lc13b2u lcd panel sharp silver tv | 2 |
rafael diagonal port hotel | 3 | diagonal knitting | 2 |
diagonal hcc hotel lutx | 3 | diagonal tile | 2 |
diagonal matrix | 2 | ||
| Source: compiled by the editor from various references; see credits. | |||
| Language | Translations for "diagonal"; alternative meanings/domain in parentheses. | |
Albanian | diagonale, diagonal. (various references) | |
Arabic | مائل (atilt, awry, bent, bevel, bias, cock eyed, inclined, oblique, sidelong, skew, slant, slanted, slantwise, slope, sloping, stooping, thwart, titled), قطري (diagonally, diametrical, native), خط مائل (slanting), خط قطري. (various references) | |
Bulgarian | диагонален (biased, biassed), диагонал. (various references) | |
Chinese | 对角. (various references) | |
Czech | diagonální, diagonála, příèný (slant, transverse, traverse), úhlopříèný, úhlopříèka. (various references) | |
Danish | diagonal (diagonal brace), skraastang (diagonal brace), skrå (bevel, inclined, oblique, skew). (various references) | |
Dutch | diagonaal (diagonal brace), schuine streep (oblique stroke, scratch, shilling stroke, slant, solidus), schuin (oblique, obscene, slanting, sloping), ophaal (separatrix, slash, solidus, stroke, virgule). (various references) | |
Esperanto | suprenstreko (separatrix, slash, solidus, stroke, virgule). (various references) | |
Farsi | مورب (Crisscross), قطر, قاطع دوزاویه , اریب (Oblique, Sidle, Slant), دوگوشه (Bicuspid). (various references) | |
Finnish | diagonaali (diagonal brace), vino (disorted, inclined, oblique, slanting), lävistäjä. (various references) | |
French | diagonale (diagonal brace). (various references) | |
German | Diagonale (diagonals), diagonal (cater-corned, diagonally). (various references) | |
Greek | διαγώνιοσ (cross), διαγώνιος ενίσχυση (diagonal brace), διαγώνιος (diagonal brace), διαγωμικός. (various references) | |
Hebrew | אלכסוני (oblique, slanted, slantwise, thwart). (various references) | |
Hungarian | átlós (cross, cross-grained, trans, transversal, transverse), átló. (various references) | |
Indonesian | diagonal, alang (crossbeam, crosswise, medium, middle). (various references) | |
Italian | diagonale (bias). (various references) | |
Japanese Kanji | 筋交い (brace, oblique), 斜交い (aslant, oblique), 斜交 (aslant, oblique), 対角線 , 対角 . (various references) | |
Japanese Katakana | たいかくせん, たいかく (accusative case, constitution, physique, tall building, the cabinet), すじかい (brace, oblique), はすかい (aslant, oblique). (various references) | |
Korean | 대각선. (various references) | |
Manx | tessenane, tessen (athwart, cross, thwart, transversal, transverse). (various references) | |
Pig Latin | iagonalday.(various references) | |
Portuguese | diagonal (diagonal brace). (various references) | |
Romanian | diagonalã (Baldric), diagonal (diagonally), oblic (aslant, asquint, athwart, bias, inclined, oblique, obliquely, sidelong, skew, slanting, sloping, splay, squint, transverse). (various references) | |
Russian | диагональный. (various references) | |
Serbo-Croatian | dijagonalan (transverse), dijagonala (bias). (various references) | |
Spanish | diagonal (cater-cornered, diagonally). (various references) | |
Swedish | diagonal. (various references) | |
Thai | เส้นทแยงมุม, ทแยงมุม. (various references) | |
Turkish | diyagonal (on the cross), köşegen (diagonal line), çapraz (across, bias, cornerwise, crisscross, cross, crossways, crosswise, decussate, groined, lattice, slantways, slantwise, thwart, transversal, transverse, traverse). (various references) | |
Ukrainian | косий (askew, awry, bevel, boss-eyed, cock eyed, cockeyed, cross-eyed, oblique, sidelong, sideway, sideways, sidewise, skew, slant, slanting, splay), діагональний, діагональ. (various references) | |
Vietnamese | đường chéo vải chéo go. (various references) | |
Welsh | lletraws. (various references) | |
| Source: compiled by the editor from various translation references. | ||
| Language | Period | Translations |
| Greek | 700 BCE-300 CE | diagonios. (various references) |
| Source: compiled by the editor from various references. | ||
Derivations | |
Words beginning with "diagonal": diagonalizable, diagonalization, diagonalizations, diagonalize, diagonalized, diagonalizes, diagonalizing, diagonally, diagonals. (additional references) | |
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"Diagonal" is suggested in spellcheckers for the following: Dagnall, Devonald, diaganal, Diagen, diagnal, Diakonia, Dianova, Digual. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "diagonal" (pronounced dīa"gunul) |
| 6 | -a" g u n u l | hexagonal, octagonal. |
| 5 | -g u n u l | polygonal. |
| 4 | -u n u l | abdominal, aberrational, aboriginal, additional, Arsenal, attitudinal, binational, biphenyl, cantonal, Cardinal, coeducational, collisional, compositional, computational, concessional, conditional, confessional, conformational, confrontational, congregational, congressional, connotational, constitutional, conventional, conversational, correctional, criminal, delusional, denominational, depositional, devotional, dimensional, directional, divisional, doctrinal, duodenal, dysfunctional, educational, emotional, erosional, exceptional, factional, fictional, fluxional, foundational, fractional, functional, gastrointestinal, generational, gravitational, impersonal, improvisational, subliminal, superregional, supranational, terminal, informational, inspirational, institutional, instructional, intentional, intergenerational, international, interpersonal, intestinal, investigational, Invitational, irrational, jurisdictional, juvenile, latitudinal, longitudinal, luminal, marginal, medicinal, motivational, multinational, national, navigational, nominal, noncriminal, nonprofessional, nontraditional, nutritional, obsessional, occasional, occupational, operational, optional, organizational, original, personal, phenomenal, processional, professional, promotional, proportional, provisional, rational, recreational, regional, relational, representational, retinal, rotational, seasonal, sectional, seminal, sensational, sentinel, situational, traditional, transformational, transitional, transnational, unconditional, unconstitutional, unconventional, unemotional, unintentional, unprofessional, untraditional, virginal, vocational. |
| 3 | -n u l | infernal, adrenal, anal, annal, annul, atonal, autumnal, carnal, channel, Colonel, communal, cornel, Darnel, departmental, diurnal, empanel, eternal, external, faunal, fennel, final, flannel, fraternal, funnel, hormonal, Hymnal, impanel, spinal, internal, journal, kennel, kernel, maternal, monoclonal, monsoonal, morainal, nocturnal, panel, paternal, penal, polyvinyl, renal, semifinal, shrapnel, signal, tonal, tribunal, tunnel, vaginal, venal, vernal, Vinal, vinyl. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
Direct Anagrams: gonadial. | |
| Words within the letters "a-a-d-g-i-l-n-o" | |
-1 letter: gonadal, loading, logania. | |
-2 letters: adagio, agnail, agonal, algoid, alodia, analog, anodal, dialog, doling, ganoid, lading, ladino, ligand. | |
-3 letters: again, aland, alang, algid, algin, align, aloin, along, danio, dingo, doing, donga, gland, gonad, gonia, indol, lagan, lanai, liana, liang, ligan, linga, lingo, logan, logia, naiad, nidal, nodal. | |
-4 letters: agin, agio, agon, alan, alga, anal, anga. | |
| Words containing the letters "a-a-d-g-i-l-n-o" | |
+1 letter: diagonals. | |
+2 letters: analogized, diagonally. | |
+3 letters: autoloading, diagnosable, diagonalize, gradational, grandiflora, railroading. | |
+4 letters: boardsailing, clapboarding, deflagration, deglaciation, diagnoseable, diagnostical, diagonalized, diagonalizes, ganglionated, grandiflorae, grandifloras, railroadings, sailboarding. | |
+5 letters: boardsailings, deflagrations, deglaciations, degranulation, diagonalizing, gradationally, prostaglandin, radiolabeling, sailboardings, undiagnosable. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
| 1. Definition 2. Synonyms 3. Crosswords 4. Usage: Commercial | 5. Images: Slideshow 6. Images: Photo Album 7. Images: Digital Art 8. Quotations: Non-fiction | 9. Usage Frequency 10. Names: Company Usage 11. Cities 12. Expressions | 13. Expressions: Internet 14. Translations: Modern 15. Translations: Ancient 16. Derivations | 17. Rhymes 18. Anagrams 19. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
