View source for Manifold

{{also|Manifold}}
==English==

===Alternative forms===
* {{alt|en|manyfold}}

===Pronunciation===
* {{IPA|en|/ˈmænɪˌfoʊld/|q2=nonstandard|/ˈmɛnɪˌfoʊld/|/ˈmɛniˌfoʊld/|a=GenAm}}
* {{IPA|en|/ˈmænɪˌfəʊld/|a=RP}}
* {{audio|en|En-us-manifold.ogg|a=US}}
* {{hyphenation|en|man|i|fold}}
* {{rhymes|en|ænɪfoʊld|s=3}}
* {{rhymes|en|əʊld|s=3}}
{{wikipedia}}

===Etymology 1===
From {{inh|en|enm|manifold}}, from {{inh|en|ang|maniġfeald|t=manifold, various, varied, complicated, numerous, abundant, plural}}, from {{inh|en|gem-pro|*managafalþaz}}, equivalent to {{suffix|en|many|fold}}. Cognate with {{cog|gmh|manecvalt|t=manifold}}, {{cog|is|margfaldr|t=multiple}}. Compare also {{cog|de|mannigfaltig|t=various}}, {{cog|nl|menigvoudig|t=various}}, {{cog|da|mangefold|t=multiple}}, {{cog|sv|mångfald|t=diversity}}.

====Adjective====
{{en-adj}}

# [[various|Various]] in [[kind#Noun|kind]] or [[quality]]; [[diverse]].
#: {{ux|en|The '''manifold''' meanings of the simple English word ''set'' are infamous among dictionary makers.}}
# [[many|Many]] in [[number#Noun|number]], [[numerous]]; [[multiple#Adjective|multiple]], [[multiplied#Adjective|multiplied]].
#* {{RQ:Book of Common Prayer|chapter=The Supper of the Lorde, and the Holy Communion, Commonly Called the Masse|folio=cxxix|passage=And although we be vnworthy (through our '''manyfolde''' ſynnes) to offre vnto thee any Sacryfice: Yet we beſeche thee to accepte thys our bounden duetie and ſeruice: and commande theſe our prayers and ſupplicacions, by the Miniſtery of thy holy Angels, to be brought vp into thy holy Tabernacle before the ſyght of thy dyuine maieſtie: {{...}}}}
# [[complicated#Adjective|Complicated]].
# [[exhibit#Verb|Exhibited]] at diverse [[time#Noun|times]] or in various [[way]]s.
#* '''c. 1384''', I Petre 4:10 ([https://web.archive.org/web/20070704203202/http://wesley.nnu.edu/biblical_studies/wycliffe/ Wycliffe's Bible]):
#*: {{...}} the '''manyfold''' grace of God.
#* '''1611''', [http://en.wikisource.org/wiki/Bible_%28King_James%29/Ephesians?oldid=448367#Chapter_3 Ephesians 3:10] ([[w:King James Bible]]):
#*: The '''manifold''' wisdom of God.

=====Synonyms=====
* {{sense|various in kind or quality}} {{l|en|diverse}}, {{l|en|various}}, {{l|en|varied}}, {{l|en|multiplicitous}}; See also [[Thesaurus:heterogeneous]]
* {{sense|many in number}} {{l|en|multiple}}, {{l|en|numerous}}; see also [[Thesaurus:manifold]]

=====Antonyms=====
* {{l|en|onefold}}
* {{l|en|singlefold}}

=====Derived terms=====
* {{l|en|manifolder}}
* {{l|en|manifoldly}}
* {{l|en|manifoldness}}

=====Translations=====
{{trans-top|various in kind or quality}}
* Arabic: {{t|ar|مُتَنَوِّع}}
* Bulgarian: {{t+|bg|разнороден}}, {{t+|bg|разнообразен}}
* Chinese:
*: Mandarin: {{t|cmn|[[雜多|雜多的]]|tr=záduō de}}
* Danish: {{t|da|mangfoldig}}
* Dutch: {{t+|nl|veelvuldig}}, {{t+|nl|talrijk}}, {{t+|nl|veelvoudig}}, {{t+|nl|divers}}
* Esperanto: {{t|eo|diversa}}, {{t|eo|pluropa|s}}
* Finnish: {{t+|fi|moninainen}}
* German: {{t+|de|vielfältig}}, {{t+|de|mannigfaltig}}, {{t+|de|verschieden}}, {{t+|de|divers}}, {{t+|de|unterschiedlich}}
* Gothic: {{t|got|𐌼𐌰𐌽𐌰𐌲𐍆𐌰𐌻𐌸𐍃}}, {{t|got|𐍆𐌹𐌻𐌿𐍆𐌰𐌹𐌷𐍃}}
* Greek: {{t|el|ποικιλόπτυχος|m}}, {{t+|el|πολλαπλός|m}}, {{t+|el|πολυειδής|m}}, {{t+|el|πολύπτυχος|m}}
*: Ancient: {{t|grc|παντοδαπός}}, {{t|grc|ποικίλος}}
* Hungarian: {{t+|hu|sokféle}}, {{t+|hu|sokfajta}}
* Italian: {{t+|it|molteplice}}, {{t+|it|multiforme}}
* Latin: {{t|la|multiplex}}
* Portuguese: {{t|pt|múltiplos|m-p}}, {{t+|pt|variados|m-p}}
* Russian: {{t+|ru|разнообра́зный}}
* Spanish: {{t+|es|múltiple}}
* Swedish: {{t+|sv|mångfaldig}}
* Tagalog: {{t+|tl|damihan}}
* Turkish: {{t+|tr|farklı}}
{{trans-bottom}}

{{trans-top|numerous, multiple, multiplied}}
* Esperanto: {{t|eo|multnombra}}
{{trans-bottom}}

{{trans-top|exhibited at diverse times or in various ways}}
* Esperanto: {{t|eo|plurfoja}}, {{t|eo|plurforma}}
* Finnish: {{t+|fi|moninainen}}
* German: {{t+|de|vielfach}}, {{t+|de|vielfältig}}, {{t+|de|wiederkehrend}}, {{t+|de|mannigfach}}
* Greek: {{t+|el|πολύμορφος|m}}
*: Ancient: {{t|grc|πολύτροπος}}
* Hungarian: {{t+|hu|sokszor}}
* Italian: {{t+|it|manifesto}}
{{trans-bottom}}

====Adverb====
{{en-adv}}

# Many times; [[repeatedly]].
#* {{quote-book|en|year=1590|author=w:Edmund Spenser|title=The Faerie Queene|others=book 1, canto 12|passage=when his daughter deare he does behold, / Her dearely doth imbrace, and kisseth '''manifold'''.}}

=====Synonyms=====
* {{l|en|manyfold}}, {{l|en|frequently}}, {{l|en|ofttimes}}; see also [[Thesaurus:often]]

====Noun====
{{en-noun}}

# {{lb|en|historical}} A [[copy]] made by the manifold writing process.
# {{lb|en|mechanics}} A pipe [[fitting]] or similar [[device]] that connects multiple [[input]]s or [[output]]s.
# {{lb|en|US|dialectal|mostly|in the plural}} The third [[stomach]] of a [[ruminant]] animal, an [[omasum]].
#* {{quote-text|en|year=1830|url=https://web.archive.org/web/20040828193511/http://www.cals.ncsu.edu/agexed/aee501/sheep.html|title=Anson, Somerset Co. Me.|accessdate=12 June 2007
|passage=My conjecture being right he will find the third stomach, or '''manifolds''', the seat of difficulty.}}
# {{lb|en|mathematics}} A [[Hausdorff]] [[topological space]] that looks [[local]]ly like the "ordinary" [[Euclidean space]] <math>\mathbb{R}^n</math>.
# {{lb|en|computer graphics}} A [[polygon mesh]] representing the continuous, closed surface of a solid object

=====Usage notes=====
* In mathematics, a manifold of some number of dimensions ''n'' is termed an ''n-manifold'' (e.g. ''3-manifold'').

=====Hyponyms=====
{{col4|en|title=(mathematics) generic families of manifolds
|Flag manifold
|Grassmann manifold
|Stiefel manifold}}

{{col4|en|title=(mathematics) manifolds definable by a particular choice of atlas
|analytic manifold
|complex manifold
|differentiable manifold
|piecewise linear manifold
|smooth manifold
|topological manifold}}

{{col4|en|title=(mathematics)  manifolds Manifolds with additional structure
|almost complex manifold
|almost symplectic manifold
|Calabi–Yau manifold
|calibrated manifold
|complex manifold
|contact manifold
|CR manifold
|Finsler manifold
|Hermitian manifold
|Hyperkähler manifold
|Kähler manifold
|Lie group
|pseudo-Riemannian manifold
|Riemannian manifold
|Sasakian manifold
|semi-Riemannian manifold
|spin manifold
|symplectic manifold}}

{{col4|en|title=(mathematics)  infinite-dimensional manifolds
|Banach manifold
|Fréchet manifold
|Hilbert manifold}}

{{col4|en|title=(mathematics) other manifolds
|[[Ck-manifold|C<sup>k</sup>-manifold]]
|[[C∞-manifold|C<sup>∞</sup>-manifold]]
|[[Cω-manifold|C<sup>ω</sup>-manifold]]
|connected manifold
|[[E8 manifold|E<sub>8</sub> manifold]]
|Einstein manifold
|Finsler manifold
|[[G2 manifold|G<sub>2</sub> manifold]]
|Kervaire manifold
|Lorentzian manifold
|manifold with boundary
|n-dimensional manifold
|n-manifold
|non-Hausdorff manifold
|non-smoothable manifold
|pure manifold
|Quaternionic Kähler manifold
|real manifold
|Ricci-flat manifold
|Spin(7) manifold
|submanifold
|Weeks manifold
|Whitehead manifold}}

=====Derived terms=====
{{col2|en|manifold writer
|chain of manifolds
|continuous manifoldness
|discontinuous manifoldness
|manifold writing
|manifoldness| Calabi-Yau manifold|inlet manifold|intake manifold|non-manifold}}

=====Translations=====
{{trans-top|copy made by the manifold writing process}}
* German: {{t+|de|Vervielfältigung|f}}, {{t+|de|Kopie|f}}
* Russian: {{t+|ru|ко́пия|f}} {{qualifier|сде́ланная копирова́льным аппара́том}}
* Turkish: {{t+|tr|teksir}}
{{trans-bottom}}

{{trans-top|pipe fitting}}
* Bulgarian: {{t+|bg|разклонение|n}}
* Catalan: {{t|ca|col·lector|m}}
* Chinese:
*: Mandarin: {{t-needed|cmn}}
* Esperanto: {{t-needed|eo}}
* Finnish: {{t|fi|jakoputki}}, {{t+|fi|jakotukki}}
* French: {{t+|fr|collecteur|m}}
* German: {{t|de|Krümmer}}, {{t+|de|Verteiler|m}}, {{t+|de|Sammler|m}}, {{t|de|Heizungsverteiler|m}}
* Greek: {{t|el|πολυσωλήνας|m}}
* Italian: {{t+|it|collettore|m}}
* Japanese: {{t-needed|ja}}
* Korean: {{t-needed|ko}}
* Norwegian:
*: Bokmål: {{t+|nb|manifold|m}}
* Polish: {{t+|pl|kolektor|m}}
* Portuguese: {{t+|pt|coletor|m}}
* Romanian: {{t-needed|ro}}
* Russian: {{t+|ru|колле́ктор|m}}, {{t+|ru|трубопрово́д|m}} {{qualifier|piping}}
* Spanish: {{t+|es|colector|m}}
* Turkish: {{t+|tr|dağıtıcı}}
{{trans-bottom}}

{{trans-see|omasum}}

{{trans-top|locally Euclidean space}}
* Catalan: {{t+|ca|varietat|f}}
* Chinese:
*: Mandarin: {{t+|cmn|流形|tr=liúxíng}}
* Czech: {{t|cs|varieta|f}}
* Danish: {{t|da|mangfoldighed|c}}
* Dutch: {{t+|nl|variëteit|f}}
* Finnish: {{t+|fi|monisto}}
* French: {{t+|fr|variété|f}}
* German: {{t+|de|Mannigfaltigkeit|f}}
* Greek: {{t|el|πολυχώρος|m}}
* Hebrew: {{t|he|יריעה טופולוגית|f}}
* Hungarian: {{t+|hu|sokaság}}
* Italian: {{t+|it|varietà}}
* Japanese: {{t+|ja|多様体|tr=tayōtai}}
* Kazakh: {{t|kk|көпбейне}}
* Macedonian: {{t|mk|многуобра́зие|n}}
* Polish: {{t+|pl|rozmaitość|f}}
* Portuguese: {{t+|pt|variedade|f}}
* Romanian: {{t+|ro|varietate|f}}
* Russian: {{t+|ru|многообра́зие|n}}
* Spanish: {{t+|es|variedad|f}}
* Swedish: {{t+|sv|mångfald|c}}
* Turkish: {{t+|tr|çok katlı}}
* Vietnamese: {{t|vi|đa tạp}}
{{trans-bottom}}

===Etymology 2===
From {{inh|en|enm|manifolden}}, from {{inh|en|ang|maniġfealdan|t=to multiply, abound, increase, extend, reward}}, equivalent to {{suffix|en|many|fold|nocat=1}}. Cognate with {{cog|gmh|manecvalten}}, {{cog|is|margfalda||to multiply}}, {{cog|sv|mångfaldiga||to manifold, reproduce}}.

====Verb====
{{en-verb}}

# {{lb|en|transitive}} To make manifold; [[multiply]].
# {{lb|en|transitive|printing}} To multiply or [[reproduce]] impressions of by a single operation.

=====Translations=====
{{trans-top|multiply}}
* Bulgarian: {{t+|bg|размножавам}}
* Czech: {{t|cs|rozmnožit}}
* German: {{t+|de|vervielfältigen}}, {{t+|de|vervielfachen}}
* Swedish: {{t+|sv|mångfaldiga}}
{{trans-bottom}}

{{C|en|Topology|Manifolds}}

==French==

===Noun===
{{fr-noun|m}}

# {{lb|fr|historical}} {{l|en|manifold}}

===Further reading===
* {{R:fr:TLFi}}