Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Symmetry |
SymmetryNoun1. (mathematics) an attribute of a shape; exact correspondence of form on opposite sides of a dividing line or plane. 2. Balance among the parts of something. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "symmetry" was first used: 1563. (references) |
| Domain | Definition |
Mechanical Engineering | The degree of equality between the servovalve normal flow gain of one polarity and that of the reversed polarity. Symmetry is measured as the difference in normal flow gain of each polarity, expressed as percentage of the greater. Source: European Union. (references) |
Mining | A. Symmetry in crystallography results from periodic repetition. A symmetry element is the geometrical locus about which a group of repeating operations acts. It may be a center, a mirror plane, or a rotation axis. b. A symmetry group is a collection of symmetry elements that may intersect at a point (point group) or that may be distributed in three-dimensional space (space group). See also:point group c. The symmetry of a fabric is the combined symmetry of all the elements making up the fabric. There are five possible symmetries: (1) spherical, for fabrics having the symmetry of a sphere; (2) axial, for fabrics having the symmetry of a spheroid; (3) orthorhombic, for fabrics having the symmetry of a triaxial ellipsoid; (4) monoclinic, for fabrics having one unique plane of symmetry; and (5) triclinic, for fabrics having no planesof symmetry. (references) |
Statistics | Implied when data values are distributed in the same way above and below the middle of the sample. Source: European Union. (references) |
Source: compiled by the editor from various references; see credits. | |
(From Wikipedia, the free Encyclopedia)
Although two objects with great similarity appear the same, they must logically be different. For example, if one rotates an equilateral triangle around its center 120 degrees, it will appear the same as it was before the rotation to an observer. In theoretical euclidean geometry, such a rotation would be unrecognizable from its previous form. In reality however, each corner of any equilateral triangle composed of matter must be composed of separate molecules in separate locations. Symmetry therefore, is a matter of similarity instead of sameness. The difficulty for an intelligence to differentiate such a seemingly exact similarity might be responsible for the mild altered state of consciousness one gets by observing intricate patterns based on symmetry.
The object with the most symmetry is empty space because any part of can be rotated, reflected or translated without apparent change.
The most familiar and conventionally taught type of symmetry is the left-right or mirror image symmetry exhibited for instance by the letter T: when this letter is reflected along a vertical axis, it appears the same. An equilateral triangle exhibits such a reflection symmetry along three axes, and in addition it shows rotational symmetry: if rotated by 120 or 240 degrees, it remains unchanged. An instance of a shape which exhibits only rotational but no reflectional symmetry is the swastika.
The German geometer Felix Klein enunciated a very influential Erlangen programme in 1872, suggesting symmetry as unifying and organising principle in geometry (at a time when that was read 'geometries'). This is a broad rather than deep principle. Initially it led to interest in the groups attached to geometries, and the slogan transformation geometry (an aspect of the New Math, but hardly controversial in modern mathematical practice). By now it has been applied in numerous forms, as kind of standard attack on problems.
A fractal, coined by Mandelbrot is symmetry involving scale. For example an equilateral triangle can be shrunk so that each of its sides are one third the length of the original's sides. These smaller triangles can be rotated and translated until they are adjacent and in the center of each of the larger triangle's lines. The smaller triangles can repeat the process, resulting in even smaller triangles on their sides. Fascinating intricate structures can be created by repeating such scaling symmetrical operations many times.
An example of a mathematical expression exhibiting symmetry is a2c + 3ab + b2c. If a and b are exchanged, the expression remains unchanged due to the commutativity of addition and multiplication.
In mathematics, one studies the symmetry of a given object by collecting all the operations that leave the object unchanged. These operations form a group. For a geometrical object, this is known as its symmetry group; for an algebraic object, one uses the term automorphism group. The whole subject of Galois theory deals with well-hidden symmetries of fields.
The generalisation of symmetry in physics to mean invariance under any kind of transformation has become one of the most powerful tools of theoretical physics. See Noether's theorem for more details. This has led to group theory being one of the areas of mathematics most studied by physicists.
See Bilateral symmetry...
See M. C. Escher
Symmetry in geometry
Symmetry in mathematics
Generalization of symmetry
If we have a given set of objects with some structure, then it is possible for a symmetry to merely convert only one object into another, instead of acting upon all possible objects simultaneously. This requires a generalization from the concept of symmetry group to that of a groupoid.Symmetry in physics
Symmetry in biology
Symmetry in art
Symmetry in literature
See also: chirality, Bilateral symmetry
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Symmetry."
Synonyms: SymmetrySynonyms: balance (n), correspondence (n), proportion (n), symmetricalness (n). (additional references) |
| Antonyms: asymmetry (n), disproportion (n). (additional references) |
| Context | Synonyms within Context (source: adapted from Roget's Thesaurus). |
Beauty | Pulchritude, form elegance, grace, beauty unadorned, natural beauty; symmetry; comeliness, fairness; Adjective: polish, gloss; good effect, good looks; belle tournure; trigness; bloom, brilliancy, radiance, splendor, gorgeousness, magnificence; sublimity, sublimification. |
Centrality | Core, kernel; nucleus, nucleolus; heart, pole axis, bull's eye; nave, navel; umbilicus, backbone, marrow, pith; vertebra, vertebral column; hotbed; concentration; (convergence); centralization; symmetry. |
Distortion | Distortion, detortion, contortion; twist, crookedness; (obliquity); grimace; deformity; malformation, malconformation; harelip; monstrosity, misproportion, want of symmetry, anamorphosis; ugliness; talipes; teratology. |
Equality | Noun: equality, parity, coextension, symmetry, balance, poise; evenness, monotony, level. |
Order | Noun: order, regularity, uniformity, symmetry, lucidus ordo; music of the spheres. |
Symmetry | Symmetry, shapeliness, finish; beauty; proportion, eurythmy, uniformity, parallelism; bilateral symmetry, trilateral symmetry, multilateral symmetry; centrality. |
Ugliness | Noun: ugliness; Adjective: deformity, inelegance; acomia; disfigurement; (blemish); want of symmetry, inconcinnity; distortion; squalor; (uncleanness). |
| Source: adapted from Roget's Thesaurus. | |
| Domain | Usage | |
Movie/TV Titles | Symmetry (1961) | |
Source: compiled by the editor from various references; see credits. | ||
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Consumer Goods | |||
Source: compiled by the editor from various references; see credits. | |||
| Thumbnail | Description & Credit | Thumbnail | Description & Credit |
 | Transmission electron micrograph of poliovirus type 1. Virions are 20-30 nm in diameter and have icosahedral symmetry. Credit: CDC. |  | Images of snowflakes showing six-sided symmetry and ice crystals. In: "Micrographia, or, Some physiological descriptions of minute bodies made by magnifying glasses....", by Robert Hooke. 1667. Call Number QH271 .H66 1667 Scheme VIII. Credit: Treasures of the Library. |
 | At large osmotic pressure long DNA fragments create a hexagonally ordered macromolecular array. Except for the symmetry of the subphase this experiment is equivalent to the multilamellar lipid subphase. Credit: NICHD. | ||
Source: pictures compiled by the editor from various references; see picture credits. | |||
| Author | Quotation |
Charles Lamb | Borrowers of books --those mutilators of collections, spoilers of the symmetry of shelves, and creators of odd volumes. |
Source: compiled by the editor from various references. | |
| Title | Author | Quote |
Les Miserables | Hugo, Victor | Nothing stifles one like this perpetual symmetry. |
Source: compiled by the editor from various references. | ||
| "Symmetry" is generally used as a noun (singular) -- approximately 100.00% of the time. "Symmetry" is used about 775 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 |
| Noun (singular) | 100% | 775 | 8,892 |
Source: compiled by the editor from several corpora; see credits.
Expressions using "symmetry": Axis of symmetry ♦ bilateral symmetry ♦ mirror symmetry ♦ multilateral symmetry ♦ radial symmetry ♦ respective symmetry ♦ serial symmetry ♦ symmetry point ♦ zonal symmetry. Additional references. | |
| Hyphenated Usage | |
Beginning with "symmetry": symmetry-adapted, symmetry-breaking, symmetry-forbidden, symmetry-related. | |
Ending with "symmetry": low-symmetry, Pseudo-symmetry. | |
| 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. |
| Language | Translations for "symmetry"; alternative meanings/domain in parentheses. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Albanian | simetri (conformation), barazi (equability, equality, equally, equilibration, evenness, par, parity). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Arabic | تماثل (community, homogeneity, identification, identify, identity, like, likeness, oneness, resemble, sameness, self identification, similarity, sympathize, uniformity), تناسق (be a match for, concent, coordination, harmony), تناسبية (proportionality), تناظر (dispute), تساوق, تعادل (balance, dead heat, draw, drawn, equality, equalize, neutralize, tie), تطابق (agree, coincide, coincidence, concurrence, consistency, correspond, correspondence, fitness, identification, identify, match, oneness, parallelism, self identification). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Bulgarian | съразмерност, симетрия (proportion). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Chinese | 對稱性 , 對稱 (symmetrical), 对称 (symmetrical). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Czech | symetrie, soumìrnost. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Danish | symmetri, stroemningssymmetri. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Dutch | symmetrie. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Esperanto | simetrio. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Farsi | مراعات نظیر, همسازی (Harmony), هم جور, هم اراستگی , قرینه (Proportion), تناسب (Analogy, Congruence, Cooridnation, Proportion, Propriety, Scale), تقارن (Parallelism, Polarity), تشابه (Correspondence, Resemblance, Similarity, Simile). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Finnish | symmetria. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
French | symétrie. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
German | Symmetrie, Gleichmaß (evenness, monotony, proportion, rate, regularity). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Greek | συμμετρία (harmony). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Hebrew | מתאם (correlation, fitting), תואם (analogue, coincidence, commensurate, compatble with, compatible, congruous, coordination, corresponding, fit, harmony, matching, suitable), תאימות (compatibility), תאימ", סימטרי". (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Hungarian | szimmetria (balance), részarányosság. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Indonesian | i'tidal (proportion). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Italian | simmetria (equability). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Japanese Kanji | 相称 , 均斉 (balance), 均整 (balance), 左右相称 , シンボル"作 (Conference of Ministers of the Group of Five, diesel, dungarees, G5, gaps between bones or muscles, gene, gene bank, gene engineering, General Infantery, genetic engineering, genius, GI, G-mark, G-men, GNP, Good design mark, government men, gross national product, jeans, jeans jacket, jeans pants, jeep, spaces, symbol manipulation, symmetric, sympathetic, symposium), 対称性 , 対称 . (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Japanese Katakana | たいしょうせい, たいしょう (a caravan, admiral, antithesis, big prize, boss, comparison, contrast, crushing victory, first prize, general, great victory, hearty laugh, imperial rescript, loud laughter, object, specific, subject, Taisho Era, target), そうしょう (contentious, dispute by legal action, general term, inheritance, master, teacher, wound), き"せい (balance, balanceof power, ban, embargo, humbly made, made of gold, prohibition, recent times, uniformity, Venus), さゆうそうしょう, シンメトリー . (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Korean | 대칭 (symmetrical). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Manx | shimmeadraght, coreggyrtys (conformity, correspondence, mutuality). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Pig Latin | ymmetrysay proporção (gear-ratio, measure, percentage, proportion, proportionable, rat, rate, ratio), harmonia (accord, accordance, arrangement, balance, chime, concord, congeniality, congruence, consistence, consistency, consonance, correspondence, diapason, harmony, keeping, music, oneness, peace, rapport, rhythm, symphony, tune, unity). (various references) simetrie. (various references) симметрия. (various references) simetrija. (various references) simetría (harmony). (various references) symmetri. (various references) การมีสั"ส่วนที่รับกัน. (various references) simetri (proportion), símetrí, uyum (accommodation, accord, accordance, balance, chime, coherence, coherency, concert, concinnity, concord, concordance, conformity, congruence, congruity, consecution, consistence, consistency, consonance, harmony, keeping, proportion, rapport, rhythm, scheme, symphony, tune, unison), bakixim, bakışım, ahenk (accord, accordance, agreement, cadence, chime, coherence, coherency, concert, concinnity, concordance, concurrence, congruence, congruity, consonance, echo, euphony, harmony, rhythm, symphony, tune, unison). (various references) симетрія. (various references) sự đối xứng, tính đối xứng cấu trúc cân đối. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Language | Period | Translations |
| Greek | 700 BCE-300 CE | symmetria. (various references) |
| Latin | 500 BCE-Modern | aequalitas, aequalitate, aequalitatem, aequitas, aequitate, aequitatem, aequitatis, concinnitas. (various references) |
| Source: compiled by the editor from various references. | ||
Derivations | |
Words ending with "symmetry": asymmetry, axisymmetry, dissymmetry, supersymmetry. (additional references) | |
| |
"Symmetry" is suggested in spellcheckers for the following: Aymestry, simetry, simmetrry, simmetry, summetry, symerty, symetrey, symetry, symmerty, symmetria, symmetrry, symmetrys. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "symmetry" (pronounced si"mutrē) |
| 7 | s i" m u t r ē | asymmetry, dissymmetry. |
| 5 | -m u t r ē | geometry, optometry, spectrometry, summitry, telemetry. |
| 4 | -u t r ē | banditry, basketry, bigotry, cabinetry, circuitry, gadgetry, helotry, idolatry, poetry, psychiatry, punditry, puppetry, rocketry, toiletry, zealotry. |
| 3 | -t r ē | ancestry, artistry, baptistery, biochemistry, carpentry, chemistry, complementary, country, dentistry, elementary, entry, forestry, gallantry, gantry, gentry, geochemistry, industry, infantry, Maestri, ministry, mitre, pageantry, palmistry, paltry, pantry, pastry, peasantry, pedantry, pleasantry, poultry, reentry, registry, sentry, sultry, tapestry, wintry. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "e-m-m-r-s-t-y-y" | |
-1 letter: mystery. | |
-2 letters: stemmy. | |
-3 letters: stymy, terms, treys, tyers, tyres. | |
-4 letters: erst, eyry, mems, rems, rest, rets, ryes, stem, stey, stye, term, trey, tyer, tyes, tyre. | |
-5 letters: ems, ers, mem, met, rem, res, ret, rye, ser, set, sty, try, tye, yes, yet. | |
| Words containing the letters "e-m-m-r-s-t-y-y" | |
+1 letter: asymmetry. | |
+3 letters: axisymmetry, dissymmetry. | |
+5 letters: supersymmetry, symmetrically. | |
| 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: Modern | 5. Usage: Commercial 6. Images: Photo Album 7. Quotations: Familiar 8. Quotations: Fiction | 9. Usage Frequency 10. Expressions 11. Expressions: Internet 12. Translations: Modern | 13. Translations: Ancient 14. Derivations 15. Rhymes 16. Anagrams | 17. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
