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. K

    Elastic Collisions in Three Dimensions

    Alrighty, I'm working on a three dimensional physics simulator that does every operation in spherical coordinates and vectors, and I'm stuck on figuring out elastic collisions. are elastic collisions essentially trading momentum between the two colliding bodies? I'm assuming not, but i can't...
  2. P

    What are the dimensions of the pointing vector in physics?

    Sorry for the trivial question. But I'm not a physics student by training and I think I running into problems due to interchanging metrical systems. S = E \times H E \equiv \frac{N}{C} H \equiv \frac{N}{A \cdot m} Also, is there any standard operator for denoted dimensions...
  3. alemsalem

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  4. F

    Calculating dimensions of power

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  5. D

    Extra Dimensions: Real or Mathematical Constructs?

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  6. J

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  7. S

    How is Velocity Distributed over 11 Dimensions?

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  8. N

    Relative Velocity in 2 Dimensions

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  9. TrickyDicky

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  10. V

    Vile spinors in odd dimensions?

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  11. B

    Linear Functions dimensions and kernels

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  12. narrator

    Understanding M-theory and Its Implications for Dimensions and Scales

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  13. A

    What Equation Predicts 10 or 11 Dimensions?

    How many dimensions are there. I can describe the first 3 spatial dimensions plus 1 of time, but all the others are a mystery. I also read that an equation predicted that there would be 10 or 11 dimensions, if this is true, what equation is that?
  14. M

    Virtual Particles And Hidden Dimensions

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  15. E

    Elastic Collision in 2 Dimensions

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  16. F

    Calculating dimensions from area and volume

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  17. R

    What are the dimensions of huygen wavelets

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  18. L

    Symmetries of Higher Dimensions & Extra Spacetimes

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  19. JK423

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  20. I

    Properties of curvature tensor in 3 dimensions?

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  21. S

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  22. B

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  23. Loren Booda

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  24. G

    A Momentum-collision problem two dimensions (HELP)

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  25. O

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  26. J

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  27. D

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  28. M

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  29. S

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  30. F

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  31. L

    Where are the missing dimensions?

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  32. L

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  33. S

    Quantum from classical behavior in higher dimensions?

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  34. Q

    Proving differentiability in two dimensions

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  35. Y

    Breaking down forces in three dimensions.

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  36. C

    Why did the other dimensions stay small in M-theory?

    From what I have gathered, M-theory states that there are 11 dimensions. We live in 4 of these dimensions, and I believe the common understanding is that the 7 other dimensions are incredibly small. At the time of the Big Bang, these 3 dimensions expanded along with the universe while the...
  37. P

    Find the dimensions of the poster that use the least amount of board

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  38. A

    How Do Track Dimensions Impact Cart Motion?

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  39. P

    MATLAB Converting Matrix Dimensions in MATLAB

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  40. C

    The Mysteries of the Other Dimensions: Uncovering the Secrets of M-Theory

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  41. Q

    What are the 26 dimensions in the M theory?

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  42. M

    Finding the work done using force vectors in 3 dimensions

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  43. H

    Path Integrals in finite dimensions

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  44. C

    Ken Ono and Hausdorff dimensions

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  45. humanino

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  46. P

    Exploring Dirac Matrices and Their Dimensions

    I am currently reading Dirac Equation from Peskin-Schroeder. In a particular para it says, "Now let us find Dirac Matrices \gamma^\mu for four-dimensional Minkowski Space. It turns out that these matrices must be at least 4X4." What is the proof of the above statement? I think (not sure)...
  47. Z

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  48. I

    How do I find the magnitude of the sum of these force vectors in 3 dimensions?

    Homework Statement [PLAIN]http://img406.imageshack.us/img406/3756/fmp1.jpg How do I calculate the magnitude of the sum of these 3 vectors? Also, how do I find the angles the sum of the vectors make with each axis? F1 = 260N F2 = 75N F3 = 60N Homework Equations F = F1 + F2 + F3The Attempt at a...
  49. A

    Optimization find dimensions problem

    Homework Statement The top and bottom margins of a poster are each 6 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 384 cm2, find the dimensions of the poster with the smallest area. Homework Equations Area of a rectangle is length...
  50. N

    Do the extra dimensions really make sense?

    Is it just me, or are dimensions supposed to simply add another coordinate, i.e., I can move 1m in x, y or z direction and be 1m away from where I started, are the dimensions in string theory based on this concept or do I not understand what a dimension is? The most confusing part is how these...
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