What is Dimensions: Definition and 1000 Discussions

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. L

    Exploring the Dimensions of Time and Space

    I'm hoping someone is willing to help me with this question. Time is well explained when observed at point between absolute rest and c. The faster an object travels through the dimension of space, the slower that object travels through the dimension of time. Fair enough. Does this...
  2. Loren Booda

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    What experiment could determine whether our universe is fractal?
  3. T

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  4. R

    Change of Variables in Multiple Dimensions

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  5. I

    Derivations of dimensions problem

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  6. R

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  7. M

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  8. D

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  9. K

    Extra Dimensions: What Caused Compactification?

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  10. K

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  11. K

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  12. S

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  13. A

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  14. S

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  15. Spinnor

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  16. K

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  17. I

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  18. L

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  19. L

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  20. T

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  21. D

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  22. P

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  23. W

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  24. Q

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  25. tom.stoer

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  26. G

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  27. F

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  28. D

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  29. L

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  30. P

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  31. X

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  32. arivero

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  33. N

    Eleven dimensions, too small or too big?

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  34. C

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  35. S

    Domain of influence for wave equation in 2 dimensions

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  36. S

    Could there be an infinite number of dimensions?

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  37. C

    Gravity across Multiple Dimensions

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  38. Fredrik

    Tell me what I'm doing wrong (velocity addition in 3+1 dimensions)

    A 3+1-dimensional Lorentz transformation can be written as \Lambda=\gamma\begin{pmatrix}1 & -v^T\beta \\ -v & \beta\end{pmatrix} where v is a 3×1 matrix representing the velocity difference, \gamma=1/\sqrt{1-v^2}, and \beta is a 3×3 matrix that's orthogonal when v=0. When \beta=I, \Lambda is...
  39. J

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    Hi everyone, I know that in P=nRT/v R = 8.314 m3*Pa/mol*k Now, when you are trying to calculate P, if you have volumn in m3 on the bottom, everything cancels out and you are left with Pa. I've just developed a simulator which simulates particle motion over time and calculates...
  40. K

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  41. B

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  42. C

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  43. K

    How Does an Airplane's Climb Affect Package Drop Distance?

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  44. B

    Are Natural Units Truly Dimensionless?

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  45. C

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  46. W

    How do I correctly calculate the height of a building using motion equations?

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  47. J

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  48. G

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  49. J

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  50. R

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