Help


[permalink] [id link]
+
Page "Spherical 3-manifold" ¶ 2
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

Spherical and 3-manifolds
The complete list of such manifolds is given in the article on Spherical 3-manifolds.

Spherical and are
Spherical concave backing surfaces support the diaphragm when excessive pressures are applied and prevent the stresses within the diaphragm from exceeding the elastic limit.
Spherical errors occur when errors have both uniform variance ( homoscedasticity ) and are uncorrelated with each other.
Spherical fullerenes are also called buckyballs, and they resemble the balls used in soccer.
Spherical mechanisms are constructed by connecting links with hinged joints such that the axes of each hinge passes through the same point.
Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of the Earth.
Spherical waves are waves whose amplitude depends only upon the radial distance r from a central point source.
Spherical geometry obeys two of Euclid's postulates: the second postulate (" to produce a finite straight line continuously in a straight line ") and the fourth postulate (" that all right angles are equal to one another ").
Spherical harmonics are often used to approximate the shape of the geoid.
Spherical harmonics are important in many theoretical and practical applications, particularly in the computation of atomic orbital electron configurations, representation of gravitational fields, geoids, and the magnetic fields of planetary bodies and stars, and characterization of the cosmic microwave background radiation.
Spherical mirrors are easier to make than parabolic mirrors and they are often used to produce approximately collimated light.
Spherical codes are higher-dimensional analogues of Tammes problem, which arose as an attempt to explain the distribution of pores on pollen grains.
which regular solutions for positive energies are given by so-called Bessel functions of the first kind ' so that the solutions written for R are the so-called Spherical Bessel function
Spherical coordinates are one of the most used curvilinear coordinate systems in such fields as Earth sciences, cartography, and physics ( in particular quantum mechanics, relativity ), engineering, etc.
Spherical tokamaks are not limited by the same instabilities as tokamaks and as such the area is receiving considerable experimental attention.
Spherical astronomy is the branch of astronomy that is concerned with where celestial objects are located and how they move on the celestial sphere.
Spherical groups with a radially fibrous structure and bristled with crystals on the surface are not uncommon.

Spherical and called
Spherical trigonometry was studied by early Greek mathematicians such as Menelaus of Alexandria, who wrote a book on spherical trigonometry called Sphaerica and developed Menelaus ' theorem.
Spherical triangles were studied by early Greek mathematicians such as Menelaus of Alexandria, who wrote a book on spherical triangles called Sphaerica and developed Menelaus ' theorem.
Spherical to ovoid concretions of rock, locally called ' kettles ', weather out of the shale along the shoreline.
When it was all completed ( in + 725 ) it was called the ' Water-Driven Spherical Bird's-Eye-View Map of the Heavens ( Shui Yun Hun Thien Fu Shih Thu ) or ' Celestial Sphere Model Water-Engine ' and was set up in front of the Wu Chheng Hall ( of the Palace ) to be seen by the multitude of officials.

Spherical and elliptic
Spherical geometry is not elliptic geometry but shares with that geometry the property that a line has no parallels through a given point.

Spherical and .
* Simon Newcomb, A Compendium of Spherical Astronomy ( Macmillan, 1906 – republished by Dover, 1960 ), 160-172.
* Thin Spherical Lenses on Project PHYSNET.
* Spherical concave and convex mirrors do not focus parallel rays to a single point due to spherical aberration.
** M. C. Escher used special shapes of mirrors in order to achieve a much more complete view of his surroundings than by direct observation in Hand with Reflecting Sphere ( also known as Self-Portrait in Spherical Mirror ).
Select this link for an animation of a Spherical deployable mechanism.
Spherical geometry is similar to elliptical geometry.
Spherical coordinates ( r, θ, φ ) as often used in mathematics: radial distance r, azimuthal angle θ, and polar angle φ.
Spherical waves coming from a point source.
Spherical objects with this surface area have a radius or diameter in the range 89, 000 km to 564, 000 km.
* Planned completion of the Five hundred meter Aperture Spherical Telescope, in China.
* Spherical sector, portion of a sphere enclosed by a cone of radii from the center of the sphere.
* SDEC Spherical Discrete Element Code.
* Chute Maven ( Hustrulid Technologies Inc .) Spherical Discrete Element Modeling in 3 Dimensions.
Spherical particles undergo less particle rearrangement than irregular particles.
Spherical stone shot were chosen because of cheapness ; forged iron, bronze and lead balls were tried, but the expense prevented their general adoption.
* Spherical coordinate system represents a point in three space by the distance from the origin and two angles measured from two reference lines which intersect the origin.
* Robin Michael Green, Spherical Astronomy.
: See also Spherical law of cosines and Half-side formula.

3-manifolds and are
Prime models and prime 3-manifolds are other examples of this type.
In three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 are non-orientable.
There are a great variety of hyperbolic 3-manifolds, and their classification is not completely understood.
The corresponding manifolds are exactly the closed 3-manifolds with finite fundamental group.
There are exactly 10 finite closed 3-manifolds with this geometry, 6 orientable and 4 non-orientable.
The first two are mapping tori of the identity map and antipode map of the 2-sphere, and are the only examples of 3-manifolds that are prime but not irreducible.
( If they are not orientable the natural fibration by circles is not necessarily a Seifert fibration: the problem is that some fibers may " reverse orientation "; in other words their neighborhoods look like fibered solid Klein bottles rather than solid tori .< ref > Ronald Fintushel, Local S < sup > 1 </ sup > actions on 3-manifolds, Pacific J. o. M. 66 No1 ( 1976 ) 111-118, http :// projecteuclid. org /...) The classification of such ( oriented ) manifolds is given in the article on Seifert fiber spaces.
Among his best known results are the solution of the classical recognition problem for 3-manifolds ( with Robert J. Daverman ) and the proof of the 4-dimensional Cellularity Criterion.
Representative topics are the structure theory of 3-manifolds and 4-manifolds, knot theory, and braid groups.
Mapping class groups of 3-manifolds have received considerable study as well, and are closely related to mapping class groups of 2-manifolds.
Handles are used to particularly study 3-manifolds.
The only compact, connected 3-manifolds that are prime but not irreducible are the trivial 2-sphere bundle over S < sup > 1 </ sup > and the twisted 2-sphere bundle over S < sup > 1 </ sup >.
The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say, topological 3-manifolds, or smooth 3-manifolds.
Using four-dimensional Cerf theory, he proved that if M and N are 3-manifolds, resulting from Dehn surgery on framed links L and J respectively, then they are homeomorphic if and only if L and J are related by a sequence of Kirby moves.

0.301 seconds.