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  Encyclopedia of Keywords > Topology > Topological Spaces > Manifolds > Dimension > Dimensions   Michael Charnine

Keywords and Sections
VERTEX
NOTION
CONCEPT
DEGREES
FREEDOM
POINT
AXIS
SIZE
SHAPE
EXTENDED
TORQUE
POLYHEDRON
VERTICES
SQUARE
SUM
POSSIBLE
UNIVERSE
EQUAL
MASS
QUANTITIES
QUANTITY
COLUMNS
MATRICES
PARTICLES
THEORIES
CURVE
SURFACES
CURVATURE
MANIFOLD
ROTATION
ANGULAR FREQUENCY
EINSTEIN
EHRENFEST
BIVECTORS
FLATLAND
LEECH LATTICE
PARTICULAR NUMBER
SUPERSTRING
SUPERSTRINGS
SIMPLE SYSTEM
MAGNITUDE
ANYON
HIGHER DIMENSION
EIGENSPACES
LORENTZ GROUP
EUCLIDEAN SPACE
Review of Short Phrases and Links

    This Review contains major "Dimensions"- related terms, short phrases and links grouped together in the form of Encyclopedia article.

Definitions

  1. Dimensions are independent components of a coordinate grid needed to locate a point in a certain defined "space". (Web site)
  2. Dimensions are components of a coordinate grid typically used to locate a point in space, or on the globe, such as by latitude, longitude and planet (Earth). (Web site)
  3. Dimensions are different for Periodicals automation flat-size mail.
  4. Such dimensions are predicted in theories with supersymmetry or superstrings. (Web site)
  5. Extra dimensions are integral to several theoretical models of the universe; string theory, for example, suggests as many as seven extra dimensions of space.

Vertex

  1. The dimensions of a cube are the lengths of the three edges which meet at any vertex. (Web site)
  2. Wythoff's construction in three dimensions is by placing a vertex in the triangle, and dropping perpendiculars to each of the edges.

Notion

  1. Regular polyhedra generalize the notion of a regular polygon to three dimensions.
  2. This is why physicists take the notion of hyperspace (10 dimensions of spacetime) seriously. (Web site)
  3. The notion of extra dimensions also helps to resolve the hierarchy problem which is the question of why gravity is so much weaker than any other force. (Web site)

Concept

  1. Briefly; a simplex is a generalization of the concept of a triangle into forms with more, or fewer, than two dimensions. (Web site)
  2. It is a generalization of the concept of a plane into a different number of dimensions. (Web site)
  3. Dimension X, an adventure game setting based on the concept of parallel universes, which are referred to as dimensions.

Degrees

  1. Furthermore, all string theories predict the existence of degrees of freedom which are usually described as extra dimensions.

Freedom

  1. Once this space has been quantized, only half of the dimensions simultaneously commute and so the number of degrees of freedom has been halved. (Web site)
  2. Counting layers gives 10 degrees of freedom (5+1+1+1+1+1 = 10), which equals the dimensions postulated by string theory. (Web site)
  3. A gas in a room have trillions of degrees of freedom if you consider all the particles individually, but only moves in 3+1 dimensions. (Web site)

Point

  1. The Big Bang theory states that it is the point in which all dimensions came into being, the start of both space and time. (Web site)
  2. The point groups in two dimensions with respect to any point leave that point fixed.
  3. The simplex in four dimensions (the pentatope) is a regular tetrahedron in which a point along the fourth dimension through the center of is chosen so that.

Axis

  1. First, it is not true in other dimensions than 3 (in a plane, a linear map that is an isometry and that keeps an axis unchanged is a reflection). (Web site)
  2. Most perceptual maps show only two dimensions at a time, for example price on one axis and quality on the other. (Web site)
  3. If you want to generalize rotations to higher dimensions, it's often much easier to think of rotations "over" a plane, instead of around a "hyper" axis. (Web site)

Size

  1. You can scale the dimensions up or down for the size and stiffness of the rope you are using.
  2. Changes might occur in size, the overall dimensions of a bone, or shape alone, such that if one dimension increases, another must decrease. (Web site)
  3. So understanding the mass of the electron is essential to understanding the size and dimensions of everything around us.

Shape

  1. Know the soul to be free of any gender and not bound by any dimensions of shape and size.
  2. In addition, in four dimensions and higher, open sets can be very different in terms of shape, size, measure, and topology, and still have the same capacity. (Web site)
  3. A Linear Collider would determine the number, size and shape of extra dimensions through their small effects on particle masses and interactions. (Web site)

Extended

  1. The concept of a vector can be extended to three or more dimensions. (Web site)
  2. The method is currently limited to potential flow in two dimensions, although the procedure can be extended to three.
  3. Therefore, vectors can be extended to three dimensions by simply adding the 'z' value.

Torque

  1. Torque has dimensions of force times distance and the SI units of torque are stated as "newton-metres". (Web site)
  2. Torque has dimensions of distance × force and the SI units of torque are stated as " newton - metres ". (Web site)
  3. Torque has dimensions of force times distance.

Polyhedron

  1. Polytope The equivalent of a polyhedron, but in any number of dimensions. (Web site)
  2. In three dimensions, stellation consists of "solidifying" parts of the extended face of a polyhedron, then repeating the same pattern for each face.

Vertices

  1. Consider the other extreme case of the complete isometric graph with n vertices, this is equivalent to the regular simplex in (n-1) dimensions. (Web site)
  2. FIG. 5A shows in two dimensions the points (vertices) 507 scanned during a typical range scan. (Web site)
  3. For example in three dimensions the vectors (v 0, v 1, v 2, v 3) are the vertices of a 3-simplex or tetrahedron.

Square

  1. Examples in two dimensions include the square, the regular pentagon and hexagon, and other regular polygons, including star polygons.
  2. The method the sphere gives to the square can be generalized so that the form of four-dimensional objects can be seen in three dimensions. (Web site)
  3. In modern terminology, the area of a plane figure is proportional to the square of any of its linear dimensions,, and the volume of a solid to the cube,. (Web site)

Sum

  1. Due to some quantum quirks, the sum of these configurations could yield a space-time with any number of dimensions.
  2. As expected then, the dimensionality of the cross product is the sum of the dimensions. (Web site)
  3. The dimension of the space is the sum of the dimensions of the two subspaces, minus the dimension of their intersection. (Web site)

Possible

  1. Conventional gravity does not place any limits on the possible dimensions of space-time: its equations can, in principle, be formulated in any dimension. (Web site)
  2. We will introduce the notion of semi-conformally flat surfaces and establish a complete classification of the possible dimensions for this family.
  3. Supersymmetry severely restricts the possible dimensions of a p-brane.

Universe

  1. According to certain Euclidean space perceptions, the universe has three dimensions of space and one dimension of time.
  2. The universe appears to have a smooth spacetime continuum consisting of three spatial dimensions and one temporal (time) dimension.
  3. Also, when thinking of space and time it is natural to ask why the universe appears to have exactly one time and three space dimensions. (Web site)

Equal

  1. If the M i are actually vector spaces, then the dimension of the direct sum is equal to the sum of the dimensions of the M i.
  2. The height and width dimensions of the foil layer are substantially equal to the dimensions of the flexible roofing material. (Web site)
  3. The divergence of the curl of any vector field (in three dimensions) is constant and equal to zero.

Mass

  1. Attachment to visualizing the dimensions precludes understanding the many different dimensions that can be measured (time, mass, color, cost, etc.). (Web site)
  2. Recall that in 3+1 dimensions, the radius of a black hole is proportional to its mass, "R=2M", in "c=hbar=G=1" Planck units.
  3. This work could reveal the secrets of dark matter, the existence of extra dimensions and explain mass and gravity.

Quantities

  1. Physical quantities in these scalar field theories may have dimensions of length, time or mass, or some combination of the three. (Web site)
  2. Some quantities which are physically different, and have different unit names, may have the same dimensions, for example, torque and work.
  3. Physical quantities having different dimensions cannot be compared to one another either.

Quantity

  1. The dimensions of a physical quantity is associated with symbols, such as M, L, T which represent mass, length and time, each raised to rational powers.
  2. The quantity A · B is the scalar valued interior product, while A ∧ B is the grade 4 exterior product that arises in four or more dimensions. (Web site)
  3. In electromagnetism, for example, it may be useful to use dimensions of M, L, T, and Q, where Q represents quantity of electric charge.

Columns

  1. Its principal ruins consisted of the propylon and two columns of a temple, which was apparently of small dimensions, but of elegant proportions.

Matrices

  1. If you want to combine rotations, in 2-D you can just add their angles, but in higher dimensions you must multiply their matrices. (Web site)
  2. Properties of the conjugate transpose (A + B) * = A * + B * for any two matrices A and B of the same dimensions.
  3. Two matrices can only be equal if they have the same dimensions and same elements.

Particles

  1. Because all of the particles feel the gravitational force, G is universal, so G can be used to form quantities with dimensions, giving the Planck scale. (Web site)
  2. Quantum Mechanics is a description that gives the best answers possible using the mathematics of only four dimensions and time and the theory of particles. (Web site)
  3. Particles are then supposed to be modes of vibration in the geometry of these extra dimensions. (Web site)

Theories

  1. This theory is nothing but an extension of Einstein Spacetime and, contrary to other theories, it requires only four dimensions: x, y, z and t. (Web site)
  2. For example, many theories of quantum gravity can create universes with arbitrary numbers of dimensions or with arbitrary cosmological constants. (Web site)
  3. It asserts that all theories that attribute more than three spatial dimensions and one temporal dimension to the world of experience are unstable.

Curve

  1. The needs of geometry, and also for example classical mechanics are to have a notion of curve in space of any number of dimensions.
  2. By "world line" we mean a curve traced out in the 4 dimensions of space-time which could be the history of a particle or a point on a shadow. (Web site)
  3. A space curve is a curve for which X is of three dimensions, usually Euclidean space; a skew curve is a space curve which lies in no plane.

Surfaces

  1. The Euler characteristic of other surfaces is a useful topological invariant, which can be extended to higher dimensions using Betti numbers.
  2. The Euler characteristic of other surfaces is a useful topological invariant, which can be extended to higher dimensions using Betti number s.
  3. The hypothesis that the unconscious is structured like a language, that is, in two dimensions, led Lacan to the topology of surfaces. (Web site)

Curvature

  1. In two dimensions, the scalar curvature is twice the Gaussian curvature, and completely characterizes the curvature of a surface.
  2. Similar operations may be extended to calculate the curvature and length of a curve and to analogous properties of surfaces in any number of dimensions. (Web site)
  3. Gaussian curvature, but only after introducing the full Riemann tensor), which is good for building intuition about curvature in higher dimensions. (Web site)

Manifold

  1. Likewise spacetime is a manifold, of four (or maybe ten or more) dimensions. (Web site)
  2. The notion of shapes like these can be generalized to higher dimensions, and such a shape is called a manifold.
  3. In dimensions two and higher, a simple but important invariant criterion is the question of whether a manifold admits a meaningful orientation.

Rotation

  1. For rotations in three dimensions, this is the axis of the rotation (a concept that has no meaning in any other dimension).
  2. Any rotation in three dimensions can be described by a rotation by some angle about some axis. (Web site)
  3. For instance, an eigenvector of a rotation in three dimensions is a vector located within the axis about which the rotation is performed.

Angular Frequency

  1. In SI units, angular frequency is measured in radians per second, with dimensions T −1 since radians are dimensionless.

Einstein

  1. Put another way, there is no such thing as absolute motion, either in the three dimensions of space, or in the fourth dimension identified by Einstein, time. (Web site)
  2. Before Einstein 's work on relativistic physics, time and space were viewed as independent dimensions.
  3. Einstein's equation says that mass literally is energy and momentum - it is the length of that vector in four dimensions. (Web site)

Ehrenfest

  1. Ehrenfest also showed that if space has an even number of dimensions, then the different parts of a wave impulse will travel at different speeds.

Bivectors

  1. In three dimensions all bivectors can be generated by the exterior product of two vectors. (Web site)
  2. While bivectors are isomorphic to vectors (via the dual) in three dimensions they can be represented by skew-symmetric matrices in any dimension. (Web site)
  3. All bivectors in two dimensions are of this form, that is multiples of the bivector e 1 e 2, written e 12 to emphasise it is a bivector rather than a vector. (Web site)

Flatland

  1. When he returns to Flatland, his preaching on the existence and significance of higher dimensions gets him thrown into prison.

Leech Lattice

  1. For example, there's a marvelous lattice in 24 dimensions called the Leech lattice, which gives the densest lattice packing of spheres in that dimension. (Web site)
  2. The 24 vertices of the 24-cell correspond to the 24 dimensions of the Leech Lattice. (Web site)

Particular Number

  1. Therefore, the photon in flat spacetime will be massless—and the theory consistent—only for a particular number of dimensions. (Web site)

Superstring

  1. These new phenomena include effects from new dimensions of space, quantum gravity, and the vibrational modes of the superstring.
  2. The bosons are again interpreted as spacetime dimensions and so the critical dimension for the superstring is 10.

Superstrings

  1. Then, in 1971, string theory incorporated supersymmetry, and this merger resulted in the creation of superstrings that can exist in ten dimensions.
  2. Many scientists, however, do not believe superstrings are the answers, because they have not detected the additional dimensions required by string theory. (Web site)
  3. The elegant universe: superstrings, hidden dimensions, and the quest for the ultimate theory.

Simple System

  1. In two dimensions, potential flow reduces to a very simple system that is analysed using complex numbers (see below).
  2. The state organisation of the Ottoman Empire was a very simple system that had two main dimensions: the military administration and the civil administration.

Magnitude

  1. Magnitude: Magnitude in three dimensions is the same as in two dimensions, with the addition of a 'z' term in the radicand.

Anyon

  1. In two dimensions the prefactor (− 1) 2 s can be replaced by any complex number of magnitude 1 (see Anyon).
  2. This misses anyon s and braid statistics in lower dimensions.

Higher Dimension

  1. Schlfli showed that there are 6 regular convex polytopes in 4 dimensions, and exactly three in each higher dimension.
  2. The calculation is the same in seven dimensions, except it is more complicated because of the higher dimension.

Eigenspaces

  1. For a square matrix A of order n to be diagonalizable, the sum of the dimensions of the eigenspaces must be equal to n.

Lorentz Group

  1. Let R = real numbers C = complex numbers H = quaternions O = octonions Let SO(n,1) denote the Lorentz group in n+1 dimensions. (Web site)
  2. The restricted Lorentz group is a connected normal subgroup of the full Lorentz group with the same dimension (in this case, 6 dimensions).
  3. The Lorentz group and the Poincare group of isometries of spacetime are Lie groups of dimensions 6 and 10 that are used in special relativity.

Euclidean Space

  1. In Euclidean space of dimensions 0, 1, 2, and 3, the simplexes are the point, line segment, triangle and tetrahedron, respectively.
  2. More general Heisenberg groups H n may be defined for higher dimensions in Euclidean space, and more generally on symplectic vector spaces.
  3. It may be embedded in Euclidean space of dimensions 4 and higher. (Web site)

Categories

  1. Topology > Topological Spaces > Manifolds > Dimension
  2. Science > Astronomy > Universe > Space
  3. Information > Science > Mathematics > Geometry
  4. Mathematics > Algebra > Linear Algebra > Vectors
  5. Science > Physics > Volume > Cube

Related Keywords

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  Short phrases about "Dimensions"
  Originally created: April 04, 2011.
  Links checked: June 17, 2013.
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