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. X

    A particle leaves the origin (motion in 2 dimensions)

    Homework Statement A particle leaves the origin with an initial velocity v = 3.92i , in m/s. It experiences a constant acceleration a = -1.00i -0.80j , in m/s2. What is the velocity of the particle when it reaches its maximum x coordinate? i-component of velocity? j-component of the...
  2. B

    Problem in equations of kinematics in two dimensions

    Problem in equations of kinematics in two dimensions..please help Hi, I'm a first year physics student and am studying equations of kinematics in two dimensions and projectile motion. I was given the following question as homework to prep for my first exam this Wednesday. I'm pretty solid on...
  3. S

    Distance formula in higher dimensions.

    Homework Statement Let A = (a_1, . . . , a_{2008}) \in \Re^{2008}, where a_i = \frac{1}{2^{i}} for each i = 1, . . . , 2008. Find the distance from the point A to the origin. Please express your answer in the form \sqrt{\frac{a}{b}} where a, b are integers. Homework Equations Extended...
  4. C

    Vector components in the 3 dimensions

    Given F = (-20i + 50j = 10k) 1. The component of the foce projected along the pole AO. 2. The magnitude of the projected component of the F along the pole AO. I have no idea where to begin, I think I need to find the angles but I'm not sure how in three dimensions. (please excuse...
  5. J

    A question on fundamental dimensions

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  6. arivero

    Brane world=non-compact extra dimensions?

    Just wondering. All this stuff of the brane world, where spacetime is a 3-brane inside a 10 dim world... is not the same than telling that we want to use non compact extra dimensions?
  7. E

    Dimensions of box with largest volume

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  8. A

    Question about Dimensions (very basic)

    1) Which of the equations below is dimension- ally correct? a. y = (2 m) cos(k x), k = 2 m-1 b. v = v0 + a x my work for: a) cos(kx) = 2ym-1 So this would lead to k = (1/x)cos-1(2ym-1) But i don't know whether the COSINE operation on RHS changes m-1 to any other unit or not. So...
  9. W

    Robertson-Walker metric in higher dimensions (and problematic Riemann tensor)

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  10. U

    Is it possible that there are organisms in higher dimensions?

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  11. W

    Maple Maple: Tensors and arbitrary dimensions

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  12. Q

    Isometry and orbit dimensions

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  13. T

    Exploring the Need for Extra Dimensions Before String Theory

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  14. J

    Hyperplanes H1 and H2 have dimensions p and q

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  15. N

    Spinors in d dimensions and Clifford algebra

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  16. A

    Is chirality operator defined in odd dimensions?

    As far as I remember, I heard from someone that the matrix \gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3 also known as the chirality operator in 3+1 dimension is not defined in odd dimensions. I do not understand why that should be the case. Suppose I am in the 4+1 dimension and I choose one...
  17. B

    Exploring the Fundamental Differences Between 3 Dimensions of Space

    Is there any fundamental difference between the 3 dimensions of space that we experience. Such as the difference that we intuitively feel between the time and space dimensions
  18. qspeechc

    Possible dimensions of eigenspaces, known characteristic polynomial

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  19. A

    Number of components of Dirac spinor in arbitrary dimensions.

    How does one calculate the number of components a Dirac spinor in arbitrary dimensions? As far as I understand, the textbooks treat the four spacetime dimensions and here the spinor has four components because the gamma matrices must be 4x4 in nature to satisfy the required algebra. Now suppose...
  20. U

    Unraveling of the extra dimensions?

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  21. U

    Curved space-time and dimensions

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  22. A

    What Are the Dimensions of a Wave Function in Various Box Problems?

    Homework Statement Does the wave function have a dimension? If it does, what are the dimensions for 1D and 2D box problems?Can you generalise this to n dimensions? Homework Equations The Attempt at a Solution Yes, it does have dimensions. For 1D box it's [tex] m^{-2} [tex]...
  23. Y

    Maxwell equations in higher dimensions

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  24. quasar987

    Something strange about uniqueness of the derivative in higher dimensions

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  25. E

    Vector Addition and Bearing Calculation in 2D Motion

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  26. A

    Unveiling the Mysteries of 14 Dimensions: Exploring String Theory and Beyond

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  27. arivero

    How many extra dimensions?

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  28. B

    Dimensions of three constants

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  29. M

    About the dimensions of the universe

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  30. E

    What Are the Dimensions of a 1x1 Unit Cell on a Cu(110) Surface?

    Hi All, Let's consider a Copper bulk material. This one can be reproduce (ad infinitum) by using a cubic unit cell (fcc) of lattice constant a. Let's cut this bulk along the (110) plane and expose the Cu(110) surface to the vacuum. My question is: which are the x and y dimensions of a (1x1)...
  31. Bob3141592

    Dimensions Curled Up: Exploring the Unknown

    What do they mean by a dimension that's curled up? I'm having a hard time with this notion. What would such a dimension be like?
  32. K

    Pauli Matrices in higher dimensions

    This has been bugging me for a while, but feel to tell me if it's a nonsensical or silly question.. Suppose there were 4 spatial dimensions instead of 3. How would we go about constructing the Pauli matrices? Assuming each matrix still only has 2 eigenvectors, we require 4, 2x2 mutually...
  33. manjuvenamma

    Units & Dimensions: Temperature in a Second

    What will be the dimensions of temperature in a particular second, say the 10th?
  34. J

    General relativity in 1+1 spacetime dimensions

    Has anyone ever analysed Einstein's equations in 1+1 spactime dimensions? It seems to me like this would provide a convenient toy model for teaching or learning general relativity. For one thing the spacetime curvature can be visualized as curvature of a 2-dimensional surface.
  35. F

    Understanding Planck's Units: Exploring Dimensions and Fundamental Forces

    Homework Statement 1. What is the meaning of Planck’s units? Hint: Compare the strength of the 4 fundamental forces. 2. Calculate the Planck’s dimensions as a function of the SI units. 3. What are the dimensions of the human being in terms of Planck dimensions?Homework Equations Plancks's...
  36. F

    I-Beam Sizes: Standard Dimensions in SI Units

    Where can I get a list of standard sizes for I beams? (Preferably in SI units, just to save me time)
  37. T

    Motion in 2 Dimensions - Inclined Plane Pulleys

    Homework Statement a Mess of 5kg is being hauled up a smooth invlined place at 30 degree to the horizontal with an acceleration of 1.5ms^-2 by mean of a string parallel to the incline: a) What is tension in the string Homework Equations Fnet= ma Rules of right angled triangles (SOC CAH...
  38. T

    Motion in 2 Dimensions - Pulleys

    Homework Statement Two masses A and B and of mass 1.6kg and 2.4kg respectively are connected be a light string which passes over a a frictionless trolley. Calculate: a) The accelaration of the 1.6kg mass. b) The tension in the string c) The net force on the 2.4kg mass d) The Kinetic Energy of...
  39. H

    Motion in two dimensions question. At wit's end.

    [SOLVED] Motion in two dimensions question. At wit's end. Hi, I'll try to keep this short. I have a Physics exam tomorrow and was doing some textbook questions and can't figure out this one problem. It's killing me! I have the answer (supplied by the back of the book), but just can't seem to...
  40. S

    Why String theory has so many dimensions

    I am no expert in the string theory, but I was curious why it has so many dimensions. After thinking about it, I think I know why. It has to do with the assumption of 2-D strings. This can be understood with an analogy. We can make any color using combinations of red, blue and yellow. If we plot...
  41. N

    What is the difference between movement in one and two dimensions

    Homework Statement Write the difference between movement in one dimension and movement in two dimensions,also which are the different types for each of these movements Homework Equations The Attempt at a Solution
  42. A

    Does a dimension have dimensions?

    new to physics and my first question first,i am a nearly newbie high school student in physics, please i would like to learn physics from the internet enough to let me think ?...also i have a question in dimensions and please anyone explain how can you measure the 4d of matter although (i...
  43. J

    Finding Dimensions and Maximum Area for Geometric Shapes

    Hey I have two questions that I do not know how to answer...help? Please try to answer at a grade 10 level! And, this isn't a homework question. 1. A yard is to be enclosed by 40 meters of fencing. If all of the fencing is used, what dimensions will result in a yard with an area of 75m^2...
  44. C

    How Does Wind Affect the Flight Time of a Plane on a Square Route?

    Homework Statement A plane flies a square route with each side 1500m in length (north, west, south then east) If a wind was blowing from the east at 20 km/h the entire trip, find the total time it will take for the plane to complete the journey, given that the plane is flying at 80 km/h...
  45. P

    Limiting factor for tube dimensions in beam delivery system

    I am currently part of a group (University) working on a project that is focused on designing a linac to find the Higgs Boson. I have a question about the the limiting factor for the tube/tunnel. Currently we have two considerations: 1) The thickness of the walls required to maintain the...
  46. F

    Dimensions of the logistic map state space and quantum chaos.

    Apologies if this is the wrong forum, but I have a pair of thematically connected questions that I can't really fit anywhere else. Please move if this is better suited to the quantum physics forums. My first question being: The Poincare-Bendixon theorem states that chaos can only occur for...
  47. P

    Prove U1+U2+U3 Theorem with Dimensions

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  48. 2

    Another motion in 2 dimensions ?

    You throw a ball toward a wall at speed 25.0 m/s and at angle 40 degrees above the horizontal . The wall is distance d=22.0 m from the release point of the ball. (a) How far above the release point does the ball hit the wall? What are the (b) horizontal and (c) vertical components of its...
  49. 2

    Finding the Velocity of a Cart at its Highest Point

    A cart is propelled over an xy plane with acceleration components ax=4.0m/s^2 and ay= -2.0m/s^2 . Its initial velocity has components Vix=8.0m/s and Viy12 m/s. In unit-vector notation, what is the velocity of the cart when it reaches its greatest y coordinate? im confused on how to get...
  50. Simfish

    Irreducibility in multiple dimensions

    So we know some of the irreducibility criteria when we have one dimension X. But what about multidimensional abstract algebra? From Dummit Foote, we get that we can pair up every power of X with the powers of Y that happen to be associated with that power of X, and then treat those powers...
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