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. A

    Spring constants from the physical dimensions of a spring

    I’d like to know if anyone has formulas for calculating the spring constant (k) of coil springs, from their physical dimensions. I bought a coil spring, suspended a 0.6 kg mass to it, observed its oscillation period at very close to 0.6 seconds, and so believed the spring constant “k” to be...
  2. T

    MHB Proof of vector dimensions using inequalities

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  3. WhiteWolf98

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  4. snoopies622

    I Do index gymnastics change a tensor's dimensions?

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  5. K

    Conservation of momentum in two dimensions

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  6. Ginosko

    B Does dimensions have the same meaning in the Quantum world?

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  7. Anne Ross

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  8. T

    Green's Theorem in 3 Dimensions for non-conservative field

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  9. Y

    MHB Find the possible dimensions for each garden

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  10. M

    I Dimensions of the double slits in comparison to the electron?

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  11. A

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  12. malak

    I Michelson interferometer dimensions

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  13. nomadreid

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  14. MathematicalPhysicist

    Renormalization in Two Dimensions

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  15. Islam Hassan

    I Physical Interpretation of Compactified Dimensions?

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  16. suhruth

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  17. pairofstrings

    I What Is the New Dimension in Complex Number Graphs?

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  18. sams

    I Dimensions of Angular and Radial Nodes

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  19. G

    B Are the 3 space dimensions "equal"?

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  20. K

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  21. T

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  22. J

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  23. A

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  24. K

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  25. R

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  26. S

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  27. Specter

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  28. I

    I Pseudotensors in different dimensions

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  29. hilbert2

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  30. Arman777

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  31. Gabriele99

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  32. Spinnor

    B String theory, Calabi–Yau manifolds, complex dimensions

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  33. paulo84

    B How does calculus relate to dimensions?

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  34. paulo84

    B Rates of Change and Multiple Dimensions

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  35. T

    B Clarification about Fractal Dimensions

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  36. V

    I Hidden dimensions and quadratic term of a free field

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  37. scottdave

    Insights Make Units Work for You - Comments

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  38. MathematicalPhysicist

    A Max number of extra dimensions

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  39. R

    I Is this book correct regarding waves in even dimensions?

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  40. M

    Dimensions of Air Drag Constants and Terminal Speed Equation

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  41. J

    I Are Dimensions Real? | Questioning Space Dimensions

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  42. K

    I Exploring the Optimal Dimensions and Materials for High Vacuum Transparent Tubes

    Hello For the purpose of the experiment, I wonder what the maximum dimensions can have a transparent tube, I thought over a diameter of 30cm and a length of 1-1,5m and from what material should such a pipe be made. I would like to get a high vacuum (about 0,2-2Pa)
  43. I

    B Dimensions of A and B are different, how to express?

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  44. M

    LaTeX Help with page dimensions in latex

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  45. M

    MHB Dimensions of a rectangular prism

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  46. T

    B Why does physics consider only 3 of 6 dimensions

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  47. N

    B Must two quantities have the same dimensions

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  48. C

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  49. N

    I Question about finding resonant box dimensions

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  50. S

    Impulse and momentum in two dimensions - velocity question

    Homework Statement Sorry for another question so soon, I am not sure if there is a limit on how many I can ask. I try to keep it to a minimum but sometimes I can't figure it out on my own. Question: In a physics lab, 0.30 kg puck A, moving at 5.0 m/s [W], undergoes a collision with 0.40 kg...
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