### What does **manifold** mean?

# Definitions for manifold

ˈmæn əˌfoʊldman·i·fold

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **manifold**.

### Princeton's WordNet

manifoldnoun

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

manifold paper, manifoldnoun

a lightweight paper used with carbon paper to make multiple copies

"an original and two manifolds"

manifoldadjective

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

manifold, multiplexverb

many and varied; having many features or forms

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

manifoldverb

make multiple copies of

"multiply a letter"

multiply, manifoldverb

combine or increase by multiplication

"He managed to multiply his profits"

### Samuel Johnson's Dictionary

Manifoldadjective

Of different kinds; many in number; multiplied; complicated.

**Etymology:***many*and*fold.*When his eyes did her behold,

Her heart did seem to melt in pleasures*manifold.**Fa. Qu.*Terror of the torments

*manifold,*

In which the damned souls he did behold.*Edmund Spenser.*If that the king

Have any way your good deserts forgot,

Which he confesseth to be*manifold,*

He bids you name your griefs.*William Shakespeare, Henry IV.*If any man of quality will maintain upon Edward earl of Glo’ster, that he is a

*manifold*traitor, let him appear.*William Shakespeare.*They receive

*manifold*more in this present time, and in the world to come life everlasting.*Luke*xviii. 30.To represent to the life the

*manifold*use of friendship, see how many things a man cannot do himself.*Francis Bacon, Essays.*They not obeying,

Incurr’d, what cou’d they less? the penalty;

And*manifold*in sin deserv’d to fall.*John Milton, Par. Lost.*My scope in this experiment is

*manifold.**Robert Boyle, on Colours.*We are not got further than the borders of the mineral kingdom, so very ample is it, so various and

*manifold*its productions.*John Woodward, Nat. Hist.*

### Wikipedia

Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional manifold, or n {\displaystyle n} -manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to an open subset of n {\displaystyle n} -dimensional Euclidean space. One-dimensional manifolds include lines and circles, but not lemniscates. Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, and also the Klein bottle and real projective plane. The concept of a manifold is central to many parts of geometry and modern mathematical physics because it allows complicated structures to be described in terms of well-understood topological properties of simpler spaces. Manifolds naturally arise as solution sets of systems of equations and as graphs of functions. The concept has applications in computer-graphics given the need to associate pictures with coordinates (e.g. CT scans). Manifolds can be equipped with additional structure. One important class of manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. 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. The study of manifolds requires working knowledge of calculus and topology.

### ChatGPT

manifold

A manifold refers to a mathematical concept that describes a space that locally resembles Euclidean space. It is a mathematical object that can be visualized as a shape with a smooth and continuous structure. In simple terms, a manifold is a collection of points that locally look like regular spaces, such as planes or curves, but may have a more complex global structure. Manifolds are extensively used in various branches of mathematics, physics, and computer science to study and model complex phenomena and spaces.

### Webster Dictionary

Manifoldadjective

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

Manifoldadjective

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

Manifoldnoun

a copy of a writing made by the manifold process

Manifoldnoun

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

Manifoldnoun

the third stomach of a ruminant animal

Manifoldverb

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

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

### Wikidata

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

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**.

### Surnames Frequency by Census Records

MANIFOLD

According to the U.S. Census Bureau,

**Manifold**is ranked**#35671**in terms of the most common surnames in America.

The**Manifold**surname appeared**630**times in the 2010 census and if you were to sample 100,000 people in the United States, approximately**0**would have the surname**Manifold**.**86%**or**542**total occurrences were**White**.**8.8%**or**56**total occurrences were**Black**.**2.7%**or**17**total occurrences were of**two or more races**.**1.2%**or**8**total occurrences were**Asian**.**1.1%**or**7**total occurrences were of**Hispanic**origin.

### Numerology

Chaldean Numerology

The numerical value of manifold in Chaldean Numerology is:

**6**Pythagorean Numerology

The numerical value of manifold in Pythagorean Numerology is:

**2**

### Examples of manifold in a Sentence

A plan is just a tangent vector on the

**manifold**of reality.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.

### Popularity rank by frequency of use

### References

## Translations for **manifold**

### From our Multilingual Translation Dictionary

- متشعبArabic
- rozmnožit, varietaCzech
- mangfoldighedDanish
- Mannigfaltigkeit, Verteiler, vielfältig, mannigfaltigGerman
- πολυσωλήνας, πολλαπλός, πολύμορφος, πολυχώρος, πολύπτυχος, πολυειδήςGreek
- variedad, múltiple, colectorSpanish
- monistoFinnish
- variétéFrench
- יריעה טופולוגיתHebrew
- sokszor, sokfajta, sokaság, sokféleHungarian
- multiforme, manifesto, molteplice, varietàItalian
- 多様体Japanese
- многуобразиеMacedonian
- variëteit, veelvoudig, talrijk, divers, veelvuldigDutch
- kolektor, rozmaitośćPolish
- variados, coletor, variedade, múltiplosPortuguese
- разнообразный, многообразие, коллектор, трубопровод, копияRussian
- mångfaldSwedish
- பன்மடங்குTamil
- çokkatlı, teksir, dağıtıcıTurkish
- کئی گناUrdu

### Get even more translations for manifold »

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"manifold." *Definitions.net.* STANDS4 LLC, 2024. Web. 23 Jul 2024. <https://www.definitions.net/definition/manifold>.

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