What is Dimension: Definition and 897 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. S

    What are the dimensions of A and B in the equation x = At2{1-exp(-t2/B)}?

    Homework Statement If x and t represent position and time, respectively, and A and B are constants in x = At2{1-exp(-t2/B)}, what are the dimensions of A and B? 2. The attempt at a solution I just slept through my first class and found that I have many homework problems related to...
  2. M

    One or more couldn't be resolved in descending dimensions

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  3. julianwitkowski

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  4. W

    Dimension in Physics: Existing vs Non-Existing Points/Events

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  5. Marceli

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  6. Xiaomin Chu

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  7. S

    Question about Space -- Is Space itself a 4th dimensional object?

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  8. T

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  9. T

    Can time have more than one dimension?

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  10. P

    Dimension Analysis and buckingham pi

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  11. M

    Exploring the Concept of Time as a Dimension in Physics

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  12. Logan Land

    MHB Find basis and dimension of the intersection of S and T

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  13. S

    One dimension conservative force and potential energy

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  14. Logan Land

    MHB Dimension and Basis of a Relation in R5

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  15. P

    Dimension of a graphical model

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  16. D

    How to find cross sectional dimension of beam

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  17. H

    Exploring the 4th Dimension: Understanding Time in Spatial Dimensions

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  18. L

    Dirac gammology - dimension of the algebra

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  19. R

    MHB Show that Q adjoin square roots of 2, 3 is a vector space of dimension 4 over Q

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  20. M

    Can the Double Slit Experiment Reveal Information About Parallel Dimensions?

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  21. S

    What is the relationship between span and dimension?

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  22. S

    Is it possible to measure Hausdorff dimension for real world objects?

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  23. V

    Heat equation in one dimension with constant heat supply

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  24. M

    Exploring the Dimensions: An Introduction to Dimension Theory

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  25. shounakbhatta

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  26. Islam Hassan

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  27. T

    Questions about the (Spatial) Fourth Dimension

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  28. A

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  29. nomadreid

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  30. J

    The heat equation in one dimension w/ ihomogeneous boundary conditions

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  31. C

    Vector S, dimension of subspace Span(S)?

    Homework Statement Consider the set of vectors S= {a1,a2,a3,a4} where a1= (6,4,1,-1,2) a2 = (1,0,2,3,-4) a3= (1,4,-9,-16,22) a4= (7,1,0,-1,3) Find the dimension of the subspace Span(S)? Find a set of vectors in S that forms basis of Span(S)? Homework Equations dimension of V = n in Rn...
  32. C

    Dimension of set S, subspace of R3?

    Homework Statement Determine whether set S = {2a,-4a+5b,4b| aε R ^ bε R} is a subspace of R3? If it is a subspace of R3, find the dimension? Homework Equations dimension= n if it forms the basis of Rn, meaning that its linear independent and span(S) = V The Attempt at a...
  33. L

    Is a Second Temporal Dimension Possible?

    Hello to everybody. I had brought up the topic of extra spatial dimension in the math sector of the forum and was directed to the physics section for a question to a second temporal dimension. My questions are the following. would a second temporal dimension run counter to the current arrow...
  34. L

    Exploring the 4th Dimension: Questions and Answers

    Hey guys here is my question. 1D = Line 2D is a plane. 3D is space. So shouldn't a fourth dimension be something else? Is there really such a thing as fourth dimensional space. There is no such thing as a 3 dimensional plane. Though you can have a 2D plane in 3D space. Next question leads to...
  35. P

    Motion in Two or Three Dimension : Projectile motion

    Homework Statement A projectile is launched at a 60° angle above the horizontal on level ground. The change in its velocity between launch and just before landing is found to be Δv→ = v→landing _ v→launch = -20 y^ m/s . What is the initial velocity of the Projectile ? What is its final...
  36. Einj

    Dimension of n-point Green function

    Hi everyone. I have a very quick question. Can someone tell me how to compute the energy dimensions of an n-point Green function. Consider for example a \lambda\phi^4 scalar theory. I know that the dimensions of an n-pt Green function are 4-n (or something like that). How do I prove it? Thanks
  37. P

    The expansion of the universe, evidence of a 4th spatial dimension?

    in order to explain the big bang theory and the expansion of space itself, people often draw upon the analogy of blowing air into a balloon and the 2 dimensional surface of the balloon expanding. isn't the 2-D balloon surface expanding in the third dimension, since the volume of the balloon is...
  38. C

    MHB Show deg of minimal poly = dimension of V

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  39. C

    Linear algebra - need to show deg of minimal poly = dimension of V

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  40. B

    Viewing the fifth dimension

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  41. J

    Average velocity in two dimension with given functions?

    Suppose that the position vector for a particle is given as a function of time by vector r (t) = x(t)i + y(t)j, with x(t) = at + b and y(t) = ct^2 + d, where a = 1.70 m/s, b = 1.05 m, c = 0.126 m/s2, and d = 1.12 m. So, I evaluated x(t) and y(t) at each time: x(t): 1.70*2.05+1.05 which...
  42. Y

    MHB Basis, dimension and vector spaces

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  43. G

    Can You Imagine a Fourth Dimension?

    Hey there peers :smile: I'm really keen on explaining science to others and I've been practicing it with my classmates lately, so I thought why not give it a try and make my first ever youtube video about a seemingly hard concept which is a space of 4 dimensions. I made this post just because...
  44. R

    Optimum dimension for a cylindrical vessel subject to external pressur

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  45. N

    Confusion regarding 2 dimension motion

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  46. M

    How cyclic coordinates affect the dimension of the cotangent manifold

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  47. A

    Does a Fourier Series Have an Infinite Dimensional Parameter Space?

    Want to understand a concept here about dimensions of a function. Using example 1: a simple Fourier series from http://en.wikipedia.org/wiki/Fourier_series s(x) = \frac{a_0}{2} + \sum ^{\infty}_{0}[a_n cos(nx) + b_n sin(nx)] So do we now say that s(x) has an infinite dimensional...
  48. M

    Fourth Dimension: Exploring What Lies Beyond

    I'm a little confused by extra dimensions. People seem to say different things about the 'extra dimensions. Everyone seems to say that there are 3 basic dimensions (width, height, depth), however some people say different things about what additional dimensions are, just wondered if someone can...
  49. dexterdev

    Ambiguity in the term 'dimension'?

    We used to classify signals as 1D and 2D etc ie one dimensional and two dimensional. For example a periodic square wave signal is 1D and an image is a 2D signal etc (reference - Signals and systems by Simon Haykin and Barry Van Veen, 2nd edition , page 2). But the same periodic square wave...
  50. L

    3 dimension reactions problem - statics

    Homework Statement A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cable DCE that passes over a frictionless hook at C. Assuming that the tension is the same in both parts of the cable, determine (a) the tension in the cable, (b) the reactions at...
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