# Definitions for manifoldˈmæn əˌfoʊldman·i·fold

### Princeton's WordNet(4.00 / 1 vote)Rate this definition:

1. manifold(noun)

a pipe that has several lateral outlets to or from other pipes

2. manifold paper, manifold(noun)

a lightweight paper used with carbon paper to make multiple copies

"an original and two manifolds"

a set of points such as those of a closed surface or an analogue in three or more dimensions

4. manifold, multiplex(verb)

many and varied; having many features or forms

"manifold reasons"; "our manifold failings"; "manifold intelligence"; "the multiplex opportunities in high technology"

5. manifold(verb)

make multiple copies of

"multiply a letter"

6. multiply, manifold(verb)

combine or increase by multiplication

"He managed to multiply his profits"

### Webster Dictionary(0.00 / 0 votes)Rate this definition:

various in kind or quality; many in number; numerous; multiplied; complicated

Etymology: [AS. manigfeald. See Many, and Fold.]

exhibited at divers times or in various ways; -- used to qualify nouns in the singular number

Etymology: [AS. manigfeald. See Many, and Fold.]

3. Manifold(noun)

a copy of a writing made by the manifold process

Etymology: [AS. manigfeald. See Many, and Fold.]

4. Manifold(noun)

a cylindrical pipe fitting, having a number of lateral outlets, for connecting one pipe with several others

Etymology: [AS. manigfeald. See Many, and Fold.]

5. Manifold(noun)

the third stomach of a ruminant animal

Etymology: [AS. manigfeald. See Many, and Fold.]

6. Manifold(verb)

to take copies of by the process of manifold writing; as, to manifold a letter

Etymology: [AS. manigfeald. See Many, and Fold.]

### Freebase(3.00 / 1 vote)Rate this definition:

1. Manifold

In mathematics, a manifold is a topological space that near each point resembles Euclidean space. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n. Lines and circles, but not figure eights, are one-dimensional manifolds. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be realized in three dimensions, but also the Klein bottle and real projective plane which cannot. Although near each point, a manifold resembles Euclidean space, globally a manifold might not. For example, the surface of the sphere is not a Euclidean space, but in a region it can be charted by means of geographic maps: map projections of the region into the Euclidean plane. When a region appears in two neighbouring maps, the two representations do not coincide exactly and a transformation is needed to pass from one to the other, called a transition map. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows more complicated structures to be described and understood in terms of the relatively well-understood properties of Euclidean space. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. Manifolds may have additional features. One important class of manifolds is the class of differentiable manifolds. This differentiable structure allows calculus to be done on manifolds. A Riemannian metric on a manifold allows distances and angles to be measured. Symplectic manifolds serve as the phase spaces in the Hamiltonian formalism of classical mechanics, while four-dimensional Lorentzian manifolds model spacetime in general relativity.

### Chambers 20th Century Dictionary(0.00 / 0 votes)Rate this definition:

1. Manifold

man′i-fōld, adj. various in kind or quality: many in number: multiplied.—adj. Man′ifolded (Spens.), having many folds or complications.—adv. Man′ifoldly.—n. Man′ifoldness.

1. Alex
US English
Daniel
British
Karen
Australian
Veena
Indian

### Numerology

1. Chaldean Numerology

The numerical value of manifold in Chaldean Numerology is: 6

2. Pythagorean Numerology

The numerical value of manifold in Pythagorean Numerology is: 2

### Examples of manifold in a Sentence

1. A plan is just a tangent vector on the manifold of reality.

2. From one Soul of the Universe are all Souls derived. . .Of these Souls there are many changes, some into a more fortunate estate, and some quite contrary. . .Not all human souls but only the pious ones are divine. Once separated from the body, and after the struggle to acquire piety, which consists in knowing God and injuring none, such a soul becomes all intelligence. The impious soul, however, punishes itself by seeking a human body to enter into, for no other body can receive a human soul it cannot enter the body of an animal devoid of reason. Divine law preserves the human soul from such infamy. . .The soul passeth from form to form and the mansions of her pilgrimage are manifold. Thou puttest off thy bodies as raiment and as vesture dost thou fold them up. Thou art from old, O Soul of Man yea, thou art from everlasting.

3. A voluntary stranding is a natural behavior of orcas living in the wild… The orcas at Loro Parque are trained to leave the water on their own accord. This behavior is used for manifold purposes, for example, for presenting the animals to the public, for conducting corporal check-ups, for inspecting their blowholes, as well as for testing hearing abilities of the orcas.

4. Basics of Macro-systems' Behavior Prediction 1 .The Macro-systems with their sometimes stochastic behavior may be (good) indicators of the dispersal of information from a holistic standpoint as well as [to be discussed later on] from a regionally molecular anisotropic zone. 2. The data scattering as for systems with quasi-vector behavior on liquids, on gases, and amongst solids, when observed from an epi-phenomenological perspective versus a phenomenological one, can show that a number of classical views on mechanistic behavior of Macro-systems may be substituted with some “machinic” view.¬ 3. The abandonment of the purely mechanistic view of interfacial forces and the adoption of thermodynamic and probabilistic concepts such as free energy and entropy have been two of the most important steps towards getting out of the worn-out mechanistic notions into more abstract conceptualization of information dispersal, working instead of causality. 4. Comparison also has to be made between hermeneutics of the notion of entropic forces within and without the framework of established thermodynamics. The very word “force” is itself a bit too collocated with entropy already. What we are after is to make it next of kin to ideas of data, information, topology of data, and mereology of stochasticity. 5. The physico-chemical potentiality inside a variety of equilibrium states can be used as a platform for anisotropic configurations whereby not only the entropy of confinement, but also the entropy of dispersal find their true meaning. 6. Within contexts of classical accumulation and energy-growth models, the verifiability of any anisotropic reversal is also demonstrable, if not by means of a set of axioms, at least by multiplicities of interfacial behavior in which experimental data find their mereotopological ratios one in the neighborhood of the other (considering first, for the sake of simplicity, our state spaces to be of metric nature). 7. Thus, there remains the reciprocity of interfacial tensions calculations where surface tension gives rise to internal polarization of those data systems by which we should like to derive either axiomatic or multiple manifoldic regionalization of PREDICTION. 8. This, with a number of Chaotic and Strange-Attractors modifications, can potentially be applied even to the whole matrix of the Universe. 9. Most of the literature on systems (information) entropy regard mesoscopic level as THE one with highest aptitude for (physicalistic) data analysis. However, there are clues to indicate that some of the main streams of structuration and dynamics are EITHER in common amongst microscopic, mesoscopic, and macroscopic systems OR holistic patterns of the said structurations and dynamics can be derived one from the other two. For example, we shall show later—in the course of the unfolding of present notions—that density functional theory (DFT) which has become the physicists’ methodology for describing solids’ electronic structure, can also be extended to other methods or systems. Few-atom systems can implicate the already explicated order of, say, biomolecules if rigorous analyses are carried out over the transition phases (translational data mappings). 10. The level of likelihood of information dispersal in any nano- and pico-systems with/without (full) attachment to and/or dependence upon chemical energy exchange, relates to dynamics of differentials of those multiplicities of tubing interconnector manifolds which potentially have the capacity to harness thermal energy. This spells that consumption of chemical energy does not necessarily always act against the infusion of energy. Here, delineation has to be made over the minutiae of the differences between Micro- and Macro-systems. Any movement of lines of demarcation throughout the said systems over the issue of (non-)interdependency of data mereotopology on chemical energy exchange, may be predicted if classical nucleation and growth theories give their place to an even more rigorous science of Differences. Repetition of (observation) of such Differences makes it possible to see through some of the most “macro” levels of systematicity [we have already run some simulations of micro-spaces’ state mappings for purposes of clarifying how many of the plasma macro jet streams inside stars or in the inter-galaxial space move. Even magneticity has turned out, with all due caution, to be comparable]. The above-said Differences actually refer to potentialities within lines of thermodynamic exchanges based upon anisotropy of information. Such exchanges nominate themselves as MO exchanges when “micro” but as some the most specific gravito-convectional currents in usages for astrology, earth science, and ecology. Thence, the science will be brought out of prognosing the detailed balance of mesoscopic (ir-)reversibility in terms of data neighborhoods connectivity. On any differentiable manifold with its own ring of universal differentiable functions, we may determine to have the “installing” of modules of Kähler spaces where demarcation could be represented by: d(a+b)=da+db, d(ab)=adb+bda, and: dλ=0(a,b∈A,λ∈k)d(a+b)=da+db,d(ab)=adb+bda,dλ=0(a,b∈A,λ∈k) Where any one module has the formalism: dbdb (b∈Ab∈A). All these having been said, again we have the problematics of still remaining within the realm of classic calculus. It is likely that for Macrosystems we may decide not to apply the classical version.

### Popularity rank by frequency of use

manifold#10000#15098#100000

## Translations for manifold

### From our Multilingual Translation Dictionary

• varieta, rozmnožit
• mangfoldighed
• Verteiler, mannigfaltig, vielfältig, Mannigfaltigkeit
• πολυσωλήνας, πολύμορφος, πολύπτυχος, πολυειδής, πολυχώρος, πολλαπλός
• monisto
• variété
• יריעה טופולוגית
• sokfajta, sokféle, sokszor, sokaság
• molteplice, varietà, manifesto, multiforme
• 多様体
• многуобразие
• talrijk, veelvuldig, variëteit, divers, veelvoudig
• kolektor, rozmaitość
• коллектор, копия, трубопровод, разнообразный, многообразие
• mångfald
• பன்மடங்கு
• teksir, çokkatlı, dağıtıcı
• کئی گنا

### Translation

#### Find a translation for the manifold definition in other languages:

Select another language:

• - Select -
• 简体中文 (Chinese - Simplified)
• Español (Spanish)
• Esperanto (Esperanto)
• 日本語 (Japanese)
• Português (Portuguese)
• Deutsch (German)
• العربية (Arabic)
• Français (French)
• Русский (Russian)
• 한국어 (Korean)
• עברית (Hebrew)
• Gaeilge (Irish)
• Українська (Ukrainian)
• اردو (Urdu)
• Magyar (Hungarian)
• मानक हिन्दी (Hindi)
• Indonesia (Indonesian)
• Italiano (Italian)
• தமிழ் (Tamil)
• Türkçe (Turkish)
• తెలుగు (Telugu)
• ภาษาไทย (Thai)
• Tiếng Việt (Vietnamese)
• Čeština (Czech)
• Polski (Polish)
• Bahasa Indonesia (Indonesian)
• Românește (Romanian)
• Nederlands (Dutch)
• Ελληνικά (Greek)
• Latinum (Latin)
• Svenska (Swedish)
• Dansk (Danish)
• Suomi (Finnish)
• فارسی (Persian)
• ייִדיש (Yiddish)
• հայերեն (Armenian)
• Norsk (Norwegian)
• English (English)

## Citation

#### Use the citation below to add this definition to your bibliography:

Style:MLAChicagoAPA

"manifold." Definitions.net. STANDS4 LLC, 2020. Web. 27 Sep. 2020. <https://www.definitions.net/definition/manifold>.

## Are we missing a good definition for manifold? Don't keep it to yourself...

#### Free, no signup required:

Get instant definitions for any word that hits you anywhere on the web!