Definitions for manifoldˈmæn əˌfoʊld
This page provides all possible meanings and translations of the word manifold
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"
a set of points such as those of a closed surface or an analogue in three or more dimensions
many and varied; having many features or forms
"manifold reasons"; "our manifold failings"; "manifold intelligence"; "the multiplex opportunities in high technology"
make multiple copies of
"multiply a letter"
combine or increase by multiplication
"He managed to multiply his profits"
various in kind or quality; many in number; numerous; multiplied; complicated
exhibited at divers times or in various ways; -- used to qualify nouns in the singular number
a copy of a writing made by the manifold process
a cylindrical pipe fitting, having a number of lateral outlets, for connecting one pipe with several others
the third stomach of a ruminant animal
to take copies of by the process of manifold writing; as, to manifold a letter
Origin: [AS. manigfeald. See Many, and Fold.]
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.
Sample Sentences & Example Usage
A plan is just a tangent vector on the manifold of reality.
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.
Translations for manifold
From our Multilingual Translation Dictionary
- varieta, rozmnožitCzech
- Verteiler, mannigfaltig, vielfältig, MannigfaltigkeitGerman
- πολυσωλήνας, πολύμορφος, πολύπτυχος, πολυειδής, πολυχώρος, πολλαπλόςGreek
- colector, variedad, múltipleSpanish
- יריעה טופולוגיתHebrew
- sokfajta, sokféle, sokszor, sokaságHungarian
- molteplice, varietà, manifesto, multiformeItalian
- talrijk, veelvuldig, variëteit, divers, veelvoudigDutch
- kolektor, rozmaitośćPolish
- variados, múltiplos, variedade, coletorPortuguese
- коллектор, копия, трубопровод, разнообразный, многообразиеRussian
- teksir, çokkatlı, dağıtıcıTurkish
Get even more translations for manifold »
Find a translation for the manifold definition in other languages:
Select another language: