Crossword clues for manifold
manifold
Longman Dictionary of Contemporary English
The Collaborative International Dictionary
Manifold \Man"i*fold\, n.
A copy of a writing made by the manifold process.
(Mech.) A cylindrical pipe fitting, having a number of lateral outlets, for connecting one pipe with several others; as, the exhaust manifold of an automobile engine.
pl. The third stomach of a ruminant animal. [Local, U.S.]
Manifold \Man"i*fold\, v. t. [imp. & p. p. Manifolded; p. pr. & vb. n. Manifolding.] To take copies of by the process of manifold writing; as, to manifold a letter.
Manifold \Man"i*fold\, a. [AS. manigfeald. See Many, and Fold.]
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Various in kind or quality; many in number; numerous; multiplied; complicated.
O Lord, how manifold are thy works!
--Ps. civ. 24.I know your manifold transgressions.
--Amos v. 1 -
2. Exhibited at divers times or in various ways; -- used to qualify nouns in the singular number. ``The manifold wisdom of God.''
--Eph. iii. 10. ``The manifold grace of God.''
--1 Pet. iv. 10.Manifold writing, a process or method by which several copies, as of a letter, are simultaneously made, sheets of coloring paper being infolded with thin sheets of plain paper upon which the marks made by a stylus or a type-writer are transferred; writing several copies of a document at once by use of carbon paper or the like.
Douglas Harper's Etymology Dictionary
Old English monigfald (Anglian), manigfeald (West Saxon), "various, varied in appearance, complicated; numerous, abundant," from manig (see many) + -feald (see -fold). A common Germanic compound (Old Frisian manichfald, Middle Dutch menichvout, German mannigfalt, Swedish mångfalt, Gothic managfalþs), perhaps a loan-translation of Latin multiplex (see multiply). Retains the original pronunciation of many. Old English also had a verbal form, manigfealdian "to multiply, abound, increase, extend."
Old English manigfealdlic "in various ways, manifoldly," from the source of manifold (adj.).
in mechanical sense, first as "pipe or chamber with several outlets," 1884, see manifold (adj.); originally as manifold pipe (1857), with reference to a type of musical instrument mentioned in the Old Testament.
Wiktionary
Etymology 1
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1 various in kind or quality, diverse 2 many in number, numerous; multiple, multiplied. 3 complicated. 4 exhibit at diverse times or in various ways. adv. Many times; repeatedly. n. 1 (context now historical English) A copy made by the manifold writing process. 2 (context mechanics English) A pipe fitting or similar device that connects multiple inputs or outputs. 3 (context US regional in the plural English) The third stomach of a ruminant animal, an omasum. 4 (context mathematics English) A topological space that looks locally like the "ordinary" Euclidean space and is Hausdorff. Etymology 2
v
1 (context transitive English) To make manifold; multiply. 2 (context transitive printing English) To multiply or reproduce impressions of by a single operation.
WordNet
adj. many and varied; having many features or forms; "manifold reasons"; "our manifold failings"; "manifold intelligence"; "the multiplex opportunities in high technology" [syn: multiplex]
n. a pipe that has several lateral outlets to or from other pipes
a lightweight paper used with carbon paper to make multiple copies; "an original and two manifolds" [syn: manifold paper]
a set of points such as those of a closed surface or and analogue in three or more dimensions
v. make multiple copies of; "multiply a letter"
combine or increase by multiplication; "He managed to multiply his profits" [syn: multiply]
Wikipedia
A manifold is an abstract mathematical space which, in a close-up view, resembles the spaces described by Euclidean geometry.
Manifold may also refer to:
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an n-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension n.
One-dimensional manifolds include lines and circles, but not figure eights (because they have crossing points which are not locally homeomorphic to Euclidean 1-space). Two-dimensional manifolds are also called surfaces. Examples include the plane, the sphere, and the torus, which can all be embedded (formed without self-intersections) in three dimensional real space, but also the Klein bottle and real projective plane which will always self-intersect when immersed in real space.
Although a manifold locally resembles Euclidean space, globally it may not. For example, the surface of the sphere is not a Euclidean space, but in a region it can be charted by means of map projections of the region into the Euclidean plane (in the context of manifolds they are called charts). When a region appears in two neighbouring charts, 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.
thumb|Industrial manifold A manifold is a wide and/or bigger pipe, or channel, into which smaller pipes or channels lead.
Types of manifolds in engineering include:
- Exhaust manifold, an engine part which collects the exhaust gases from multiple cylinders into one pipe
- Hydraulic manifold, a component used to regulate fluid flow in a hydraulic system, thus controlling the transfer of power between actuators and pumps
- Inlet manifold or "intake manifold", an engine part which supplies the air or fuel/air mixture to the cylinders
- Manifold (scuba), in a scuba set, connects two or more diving cylinders
- Vacuum gas manifold, an apparatus used in chemistry to manipulate gases
- Many dredge pipe pieces
In biology manifolds are found in:
- Cardiovascular system - blood vessel manifolds etc.
- Lymphatic system
- Respiratory system
Manifolds are used in:
- Pipe organ
Manifold was a mathematical magazine published at the University of Warwick. Its philosophy was "It is possible to be serious about mathematics, without being solemn." Its best known editor was the mathematician Ian Stewart who edited the magazine in the late 1960s.
A 1969 edition of the magazine mentioned a game called " Finchley Central", which became the basis for the game of Mornington Crescent as popularised by the BBC Radio 4 panel game I'm Sorry I Haven't a Clue.
In 1983 the magazine was reincarnated as 2-Manifold.
Usage examples of "manifold".
However, Professor Schleiermacher was a specimen of that noble type of scientific men to whom gold was merely the rare metal Au, and diamonds merely the element C in the scarcest of its manifold allotropic embodiments.
Sinbad came ashore there and had manifold adventures, and numberless wrecks bestrewed the sands.
A master horologe, whose duty it was to determine the intime of returning pilots according to complicated formulae weighting Einsteinian time distortions against the unpredictable deformations of the manifold, had told me that Soli had aged one hundred and three years this last journey and would have died but for the skills of the Lord Cetic.
Thus with his brain full of manifold and multiform thoughts of the past did Cormac mac Art sit and wallow in days gone by, and avoid thereby thinking of the present and future.
He had eye and thought only for the tremendous panorama passing before him, where everything was clear and visible, as if it were an act in some old Roman circus, magnified manifold.
Being-with-Unity it would be a manifold, whereas in the pure Unity there is no Being save in so far as Unity attends to producing it.
No one could tell me how they had once piloted their deep ships and scurfed the windows of the manifold because no one remembered.
All, in so far as, departing from that perfect Singleness which can be measured by no other Singleness, it became, to a certain extent, manifold, though still Absolute and Perfect.
The big Avenger slanted down, the wind noise increasing in pitch and volume, and Phillips with his left hand, not looking, retrimmed it for the power glide and occasionally pulled the throttle back slightly to keep the manifold pressure from building up.
When a pilot returns from the manifold years older or younger than his lover, as Soli recently had, the differential aging-we call it crueltime-can destroy them.
In one of them, just before Soli destroyed them, Bardo and Justine opened a window to the manifold and fled the battle.
Here the reference of a theologoumenon to a passage of Scripture was of itself sufficient, and the manifold and incongruous doctrines were felt as a unity in so far as they could all be verified from Holy Scriptures.
For, notwithstanding the manifold reasons he had to expect a happy issue to his aim, his imagination was incessantly infected with something that chilled his nerves and saddened his heart, recurring, with quick succession, like the unwearied wave that beats upon the bleak, inhospitable Greenland shore.
Each was a potent bacteriacide but in combination their action was multiplied manifold.
Little in mathematics beyond the elementary level of calculus of variations, and nothing at all about Banach algebra or Riemannian manifolds.