manifold

See also: Manifold

English

Alternative forms

• manyfold

Pronunciation

• (General American) IPA^(key): /ˈmænɪˌfoʊld/, (nonstandard) /ˈmɛnɪˌfoʊld/, /ˈmɛniˌfoʊld/
• (Received Pronunciation) IPA^(key): /ˈmænɪˌfəʊld/

• Audio (US)

  (file)

• Hyphenation: man‧i‧fold
• Rhymes: -ænɪfoʊld

Etymology 1

From Middle English manifold, from Old English maniġfeald (“manifold, various, varied, complicated, numerous, abundant, plural”), from Proto-Germanic *managafalþaz, equivalent to many +‎ -fold. Cognate with Middle High German manecvalt (“manifold”), Icelandic margfaldr (“multiple”). Compare also German mannigfaltig (“various”), Dutch menigvoudig (“various”), Danish mangefold (“multiple”), Swedish mångfald (“diversity”).

Adjective

manifold (comparative more manifold, superlative most manifold)

1. Various in kind or quality; diverse.

   The manifold meanings of the simple English word set are infamous among dictionary makers.

2. Many in number, numerous; multiple, multiplied.
   • 1549 March 7​, Thomas Cranmer [et al.], compilers, “The Supper of the Lorde, and the Holy Communion, Commonly Called the Masse”, in The Booke of the Common Prayer and Administration of the Sacramentes, […], London: […] Edowardi Whitchurche […], OCLC 56485293, folio cxxix, recto:

     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: […]

3. Complicated.
4. Exhibited at diverse times or in various ways.
   • c. 1384, I Petre 4:10 (Wycliffe's Bible):

     ... the manyfold grace of God.

   • 1611, Ephesians 3:10 (w:King James Bible):

     The manifold wisdom of God.

Synonyms

• (various in kind or quality): diverse, various, varied, multiplicitous; See also Thesaurus:heterogeneous
• (many in number): multiple, numerous; see also Thesaurus:manifold

Antonyms

• onefold
• singlefold

Derived terms

• manifolder
• manifoldly
• manifoldness

Translations

various in kind or quality

• Arabic: مُتَنَوِّع‎ (mutanawwiʿ)
• Bulgarian: разнороден (bg) (raznoroden), разнообразен (bg) (raznoobrazen)
• Danish: mangfoldig
• Dutch: veelvuldig (nl), talrijk (nl), veelvoudig (nl), divers (nl)
• Finnish: moninainen (fi)
• German: vielfältig (de), mannigfaltig (de), verschieden (de), divers (de), unterschiedlich (de)
• Gothic: 𐌼𐌰𐌽𐌰𐌲𐍆𐌰𐌻𐌸𐍃 (managfalþs), 𐍆𐌹𐌻𐌿𐍆𐌰𐌹𐌷𐍃 (filufaihs)
• Greek: ποικιλόπτυχος m (poikilóptychos), πολλαπλός (el) m (pollaplós), πολυειδής (el) m (polyeidís), πολύπτυχος (el) m (polýptychos)

  Ancient: παντοδαπός (pantodapós), ποικίλος (poikílos)

• Hungarian: sokféle (hu), sokfajta
• Italian: molteplice (it), multiforme (it)
• Latin: multiplex
• Portuguese: múltiplos m pl, variados (pt) m pl
• Russian: разнообра́зный (ru) (raznoobráznyj)
• Spanish: múltiple (es)
• Swedish: mångfaldig (sv)
• Tagalog: damihan (tl)

exhibited at diverse times or in various ways

• Finnish: moninainen (fi)
• German: vielfach (de), vielfältig (de), wiederkehrend (de), mannigfach (de)
• Greek: πολύμορφος (el) m (polýmorfos)

  Ancient: πολύτροπος (polútropos)

• Hungarian: sokszor (hu)
• Italian: manifesto (it)

Adverb

manifold (comparative more manifold, superlative most manifold)

1. Many times; repeatedly.
   • 1590, Spenser, Edmund, The Faerie Queene, book 1, canto 12:

     when his daughter deare he does behold, / Her dearely doth imbrace, and kisseth manifold.

Synonyms

• manyfold, frequently, ofttimes; see also Thesaurus:often

Noun

manifold (plural manifolds)

1. (historical) A copy made by the manifold writing process.
2. (mechanics) A pipe fitting or similar device that connects multiple inputs or outputs.
3. (US, dialectal, chiefly in the plural) The third stomach of a ruminant animal, an omasum.
   • 1830 Anson, Somerset Co. Me., accessed 12 June 2007

     My conjecture being right he will find the third stomach, or manifolds, the seat of difficulty.

4. (mathematics) A topological space that looks locally like the "ordinary" Euclidean space $\mathbb {R} ^{n}$ and is Hausdorff.
5. (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

(mathematics) generic families of manifolds

• Flag manifold
• Grassmann manifold
• Stiefel manifold

 

(mathematics) manifolds definable by a particular choice of atlas

• analytic manifold
• complex manifold
• differentiable manifold
• piecewise linear manifold
• smooth manifold
• topological manifold

 

(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

 

(mathematics) infinite-dimensional manifolds

• Banach manifold
• Fréchet manifold
• Hilbert manifold

 

(mathematics) other manifolds

• C^k-manifold
• connected manifold
• C^ω-manifold
• C^∞-manifold
• E₈ manifold
• Einstein manifold
• Finsler manifold
• G₂ 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

• chain of manifolds
• continuous manifoldness
• discontinuous manifoldness
• manifoldness
• manifold writing

 

Translations

copy made by the manifold writing process

• German: Vervielfältigung (de) f, Kopie (de) f
• Russian: ко́пия (ru) f (kópija) (сде́ланная копирова́льным аппара́том)

• Turkish: teksir (tr)

pipe fitting

• Bulgarian: разклонение (bg) n (razklonenie)
• Chinese:

  Mandarin: please add this translation if you can

• Esperanto: please add this translation if you can
• Finnish: jakoputki, jakotukki (fi)
• French: collecteur (fr) m
• German: Verteiler (de) m, Sammler (de) m, Heizungsverteiler m
• Greek: πολυσωλήνας m (polysolínas)
• Italian: collettore (it) m

• Japanese: please add this translation if you can
• Korean: please add this translation if you can
• Polish: kolektor (pl) m
• Portuguese: coletor (pt) m
• Romanian: please add this translation if you can
• Russian: колле́ктор (ru) m (kolléktor), трубопрово́д (ru) m (truboprovód) (piping)
• Spanish: colector (es) m
• Turkish: dağıtıcı (tr)

omasum — see omasum

locally Euclidean space

• Chinese:

  Mandarin: 流形 (zh) (liúxíng)

• Czech: varieta f
• Danish: mangfoldighed c
• Dutch: variëteit (nl) f
• Finnish: monisto (fi)
• French: variété (fr) f
• German: Mannigfaltigkeit (de) f
• Greek: πολυχώρος m (polychóros)
• Hebrew: יריעה טופולוגית‎ f

• Hungarian: sokaság (hu)
• Italian: varietà (it)
• Japanese: 多様体 (tayōtai)
• Kazakh: көпбейне (köpbeyne)
• Macedonian: многуобра́зие n (mnoguobrázie)
• Polish: rozmaitość (pl) f
• Portuguese: variedade (pt) f
• Russian: многообра́зие (ru) n (mnogoobrázije)
• Spanish: variedad (es) f
• Swedish: mångfald (sv) c
• Turkish: çok katlı (tr)

Etymology 2

From Middle English manifolden, from Old English maniġfealdan (“to multiply, abound, increase, extend, reward”), equivalent to many +‎ -fold. Cognate with Middle High German manecvalten, Icelandic margfalda (“to multiply”), Swedish mångfaldiga (“to manifold, reproduce”).

Verb

manifold (third-person singular simple present manifolds, present participle manifolding, simple past and past participle manifolded)

1. (transitive) To make manifold; multiply.
2. (transitive, printing) To multiply or reproduce impressions of by a single operation.

Translations

multiply

• Bulgarian: размножавам (bg) (razmnožavam)
• Czech: rozmnožit

• German: vervielfältigen (de), vervielfachen (de)
• Swedish: mångfaldiga (sv)