Dimensions Definition and 1000 Threads

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.
In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions (4D) of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. 10 dimensions are used to describe superstring theory (6D hyperspace + 4D), 11 dimensions can describe supergravity and M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space.
The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.

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  1. A

    Dimensions Models and String Theory

    Right, Hello, I am new to this, and do not have much understanding, but can someone here help explain the Dimension Models and String theory to me?
  2. L

    Multiple Dimensions in Quantum Theories

    Will someone please explain to me how a theory, such as a quantum field theory, be expressed in more than three dimensions? Is this referring to the spatial dimensions we live in now, or what? And how does someone even begin to ponder these multiple dimensions?
  3. G

    Dimensions of Matrices Range (equalities).

    Hello everyone, I’d like to find the following range equalities: Considering the following: A=B+C \\ A=B.C^T \\ A=[ B^T C^T ]^T I would like to find the function f for each equality above. .\\ dim( R(A) ) = f( R(B) , R(C) )\\ Considere that all matrices have compatible...
  4. D

    Finding the work done using force vectors in 3 dimensions

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  5. Y

    Classical Nucleation theory two dimensions

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  6. MathematicalPhysicist

    Why the limitation on the number of dimensions?

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  7. I

    MHB Fermat's theorem (stationary points) of higher dimensions

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  8. H

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  9. M

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  10. A

    Quantum mechanics in multiple dimensions

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  11. P

    What Are the Different Dimensions of Sound and How Can They Be Distinguished?

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  12. H

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  13. P

    How Do Tire Width and Diameter Affect Vehicle Performance?

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  14. W

    Simple problem with vectors in 3 dimensions

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  15. E

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  16. K

    6th Dimensions in a 3 Dimensional universe

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  17. E

    Isomorphisms have the same dimensions

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  18. Q

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  19. S

    Exploring Cosmic Strings: Dimensions & Gravitons

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  20. I

    How Does a Particle's Position Change with Acceleration in the XY Plane?

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  21. H

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  22. lpetrich

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  23. K

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  24. S

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  25. S

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  26. T

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  27. V

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  28. karush

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  29. K

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  30. A

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  31. L

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  32. J

    Exploring 4 Dimensions: Uses of the Fourth Dimension in Analysis

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  33. R

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  34. T

    Closed Dimensions: Metric Tensor, Curvature & Time

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  35. Z

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  36. M

    Determining optimum flywheel dimensions

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  37. lpetrich

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  38. T

    [Analysis] Derivative in Two Dimensions.

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  39. K

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  40. J

    Non-integer value of dimensions?

    Given that string theory is built on the idea of one-dimensional entities, which seems much too "nice" given the general fuzziness of interpreting quantum mechanics, would it be possible for a universal theory to be based on a non-integer number of dimensions? I basically know nothing of...
  41. E

    Length of a line in 3 dimensions

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  42. C

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    I am a little confused about dimensions, if the nullspace of a matrix is spanned by the 0 vector, does that mean the dimension of the nullspace of this matrix is 0? In the problems I attached, both A and B reduced to the identity matrix. Note (2) is supposed to be dim(N(B)) and dim(col(B))...
  43. Q

    Motion in two dimensions please?

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  44. F

    What is [itex]{\delta ^n}(f(x))[/itex] in n dimensions?

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  45. qpwimblik

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  46. F

    Do wormholes require higher dimensions?

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  47. M

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  48. R

    Could Electrons Exist in 4 Dimensions?

    Greetings, This is basically just an observation I expect it to be laughed at (already has been laughed at in the mensa forum) but you know what they say - the only stupid questions are the ones left unasked and what better way to put it to rest than to ask some real hard core physicists... I...
  49. P

    Any method to find the tank size without knowing the dimensions?

    hello.i need to add chlorine to an OVERHEAD water tank.for that i need to know the proper quantity of chlorine to be added.and for that i need to know the tank capacity.unfortunately i do not know the dimensions of the tank,neither i have drawing of it..BUT...a vertical inline pump sucks water...
  50. P

    Dimensions of Intersection of Matrices S and T

    I've attached the problem. For S: I form the matrix: 1 0 0 1 0 0 0 0 Thus the dimension is 2. For T: I form the matrix 0 0 1 0 0 1 0 0 Thus the dimension is also 2. Is that the correct idea? Also what does S ∩ T mean? I couldn't find the symbol in my textbook.
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