# Definitions for **manifold**ˈmæn əˌfoʊld

### This page provides all possible meanings and translations of the word **manifold**

### Random House Webster's College Dictionary

man•i•fold^{*}ˈmæn əˌfoʊld(adj.)

of many kinds; numerous and varied:

manifold duties.

having numerous different parts, features, or forms:

a manifold social program.

using or operating similar or identical devices at the same time.

being such for many reasons:

a manifold enemy.

(n.)something having many different parts or features.

a carbon copy; facsimile.

a pipe or fitting with several openings for funneling the flow of liquids or gases, as in the exhaust system of an automobile engine.

**Category:**Machinery, Automotivea set of elements having in common a number of topologic properties.

**Category:**Math(adv.)very much; in great measure:

to multiply burdens manifold.

**Category:**Common Vocabulary(v.t.)to make copies of, as with carbon paper.

** ^{*}** Syn: See many.

#### Origin of **manifold**:

bef. 1000; ME; OE manigf(e)ald

man′i•fold`ness(n.)

### Princeton's WordNet

manifold(noun)

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

manifold paper, manifold(noun)

a lightweight paper used with carbon paper to make multiple copies

"an original and two manifolds"

manifold(adj)

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

manifold, multiplex(verb)

many and varied; having many features or forms

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

manifold(verb)

make multiple copies of

"multiply a letter"

multiply, manifold(verb)

combine or increase by multiplication

"He managed to multiply his profits"

### Webster Dictionary

Manifold(adj)

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

Manifold(adj)

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

Manifold(noun)

a copy of a writing made by the manifold process

Manifold(noun)

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

Manifold(noun)

the third stomach of a ruminant animal

Manifold(verb)

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

### Freebase

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.

# Translation

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

Select another language:

#### Discuss these manifold definitions with the community:

# Citation

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

"manifold." *Definitions.net.* STANDS4 LLC, 2014. Web. 29 Jul 2014. <http://www.definitions.net/definition/manifold>.