Dimension Definition and 906 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. H

    4+1D Flight

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  2. H

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  3. arivero

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  4. billtodd

    A Scalars, Vectors, Matrices,Tensors, Holors....

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  5. G

    B 4th spatial dimension thought experiment

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  6. J

    I How can the Universe know when you change directions?

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  7. S

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  8. Euge

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  9. S

    I Color charge is not scalar -- do their components have dimensions?

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  10. chwala

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  11. T

    I Dimension of a vector space and its subspaces

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  12. Z

    A How to add higher dimensional operator at higher energy in SM?

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  13. Z

    A Dimension of terms in Lagrangian

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  14. P

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  15. V

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  16. Safinaz

    A The scale of an extra dimension

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  17. S

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  18. H

    Vector space of functions defined by a condition

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  19. O

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  20. J

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  21. ergospherical

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  22. pellis

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  23. patric44

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  24. P

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  25. B

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  26. Labyrinth

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  27. JD_PM

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  28. DaniV

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  29. Paige_Turner

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  30. Paige_Turner

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  31. MahdiI84

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  32. V

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  33. patric44

    I Dimension of a Linear Transformation Matrix

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  34. F

    MATLAB Can I calculate the covariance matrix of a large set of data?

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  35. DaniV

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  36. potassium_mn04

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  37. G

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  38. L

    I Double delta potential -- Degeneracy of bound states in one dimension?

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  39. L

    A Dimension of \lambda constant in \delta potential

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  40. B

    I Dimension of an Angle: Clarifying the SI Standard

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  41. hquang001

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  42. Mr Davis 97

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  43. S

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  44. chucho11028

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  45. F

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  46. N

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  47. K

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  48. K

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  49. L

    I Intersection of a 4D line and a 3D polyhedron in 4D

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  50. J

    I Three equations of planes, dimension should be 1?

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