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. P

    Good problem on motion in one dimension

    PLEASE SOLVE THIS WITHOUT USING THE CALCULUS a man starts walking from a point P. after t seconds another man starts from the same point. they reach the nearer end af a bridge such that the time interval between them is T seconds. the length of the bridge is L meters. they reach the other...
  2. J

    Speed of Motorboat Going Downstream at Point 'a': 6 km/hr

    A Motorboat Going Downstream Overcame A Raft At Point 'a' . 60 Minutes Later It Turned Back And After Some Time Passed The Raft At A Distance 6 Kilometer From Point 'a'.find The Flow Velocity Assuming The Duty Of Engine To Be Constant
  3. B

    Find the Shortest Distance Between Two Lines: L1 and L2

    Hi, Can someone help me with this: What is the shortest distance between the two lines: L1: r= (1,0,0) +t( 2,3,4) L2 u= (2,1,0) +s(1,2,0) Thank you very much for your help B
  4. M

    How Far Will You Go Before Stopping? Can You Avoid Hitting the Dog?

    You are driving your new sports car at a velocity of 90km/hr, when you suddenly see a dog step into the road 50m ahead. You hit the brakes hard to get maximum deceleration of 7.5m/s^2. How far will you go before stopping? Can you avoid hitting the dog? I got 540m, which I know is wrong. V=0...
  5. T

    Complex Plane Dimension Number

    What dimension between space-time and 11 Dimensions is allocated to the complex plane 'visualized' and used in complex number theory? Complex numbers are used in every branch of maths and physics, based on an imaginary complex plane, z = x +iy where y is an imaginary axis and i^2=-1. - It's...
  6. S

    Calculating Acceleration and Displacement in 1D Motion

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  7. B

    Solving Dimension Matching Problem with Brad - 65 Characters

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  8. S

    Confused about fourth spatial dimension

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  9. S

    Is Time the Same for All Observers in Different Dimensions?

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  10. C

    General Questions: Motion in One Dimension

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  11. A

    Kinematics - One Dimension Problem

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  12. S

    Understanding Dimensions: The Interplay of Mathematics and Philosophy

    yes I have read the wikipedia definition and followed my nose around to see how it gets interpreted in various models and theories but it doesn't say why it is that when 3 come together it forms a sphere and creates an instant of time ? how can one dimension exist independently of others and...
  13. E

    Help Me Relative Motion In One Dimension.

    Help Me...Relative Motion In One Dimension. What Is the relative motion in one dimention? Drive the Acceleration equation.
  14. C

    Calculating Acceleration from Change in Velocity and Distance

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  15. C

    Three dimension space and one dimension time means

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  16. E

    Linear Transformation: Kernel, Dependence, Dimension, Basis

    This is probably a simple question, but just to be sure: if the kernel of linear transformation is {0}, then the set is linearly dependent since 0-vector is LD, right? So dimension is 0, right? Then what's the basis of kernel? No basis? thanks in advance.
  17. B

    Inelastic Collisions in One Dimension

    Here's my problem: Car A (mass 970 kg) is stopped at a traffic light when it is rear-ended by car B (mass 1600 kg). Both cars then slide with locked wheels until the frictional force from the slick road (with a low mk of 0.23) stops them, at distances dA = 5.8 m and dB = 3.6 m. What are the...
  18. D

    Funny definition of dimension of a topological space

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  19. S

    Dimension, what does this mean?

    Dimension, what does this mean?! and Has anyone heared about 2-d matter?
  20. S

    What is the Definition and Significance of Dimension in Mathematics?

    Has the Dimension a mathematical defination?
  21. B

    Dimension of matrices problems

    I'm having trouble with some matrices questions, can someone please help me? A = \left[ {\begin{array}{*{20}c} 1 & 2 & 3 & 1 \\ 2 & 4 & 8 & { - 2} \\ { - 5} & { - 10} & { - 19} & 3 \\ \end{array}} \right] B = \left[ {\begin{array}{*{20}c} 1 & 2 & 0 & 7 \\ 0 &...
  22. S

    Kinematics in one dimension

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  23. F

    Why are dimension > 4 operators non-renormalizable?

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  24. D

    Nontrivial Subspace with Equal Dimensions: Linear Algebra Example

    Hi, I'm just learning for my linear algebra exam and I wonder if somebody could give me an example of a nontrivial subspace which has as many dimensions as the original space. Thanks a lot
  25. D

    Can a Nontrivial Subspace Have the Same Dimension as Its Original Space?

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  26. G

    Are Other Dimension Universes Plausible?

    I mean is it somewhat science or is it purely sci-fi?
  27. M

    Dimension of Soln Space of Heat Equation: Is It Infinite?

    What is the dimension of soln space of the heat equation: \frac{\partial U }{\partial t}=a^2\frac{\partial^2 U}{\partial x^2} U(0,t) = U(L,t) = 0 U(x,0)= f(x) Is it infinite , if so why?
  28. marcus

    The running of the spacetime dimension (AJL)

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  29. D

    Kinematics in one dimension (easy problem)

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  30. S

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  31. M

    Relativistic velocity in the time dimension

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  32. S

    What is a black hole in 4th dimension looks like?

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  33. JamesU

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  34. T

    Thoughts on visualizing the 4th dimension

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  35. E

    Understanding Multiplicity and Dimension in Eigenvectors

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  36. JamesU

    Can we comprehend the 4th dimension.

    If we exclude time as the fourth dimension, is it possible that over many years of trial and study, that our thee-dimensional brains can comprehend a higher dimension? :bugeye:
  37. S

    Can Dimension and Time be quantized?

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  38. E

    How many 3D cubes can fit inside a hypercube in R^4?

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  39. A

    Volumes in the 4th spatial dimension

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  40. G

    8 Dimension creatures roaming the universe?

    Does this mean there are 8 Dimension creatures roaming the universe?
  41. N

    What do we call the dimension measured with time?

    I am told time is a dimension, indeed the 4th dimension but then I am also told time is effected by other things such as gravity These two seem to be at odds with each other. the three classical dimensions are length breadth and width. yet no one I know of argues that gravity or any...
  42. N

    Green fuktion on the wave operator in 1 dimension

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  43. T

    Is universal time the 4th or 5th Dimension?

    Is universal "time" the 4th or 5th Dimension? Do we live in a 4 or 5 Dimensional Universe? If Einstein had been told before writing SG and GR, that we live in a 5 Dimensional Universe, in which we can only see or detect the properties of the 4th Dimension, at speeds approaching the light...
  44. S

    Is it possible to have infinite amount of dimension?

    Quote: "Because gravity also spreads outside spacetime, only a fraction of its strength is available inside spacetime, and this is given as the explanation of why gravitation is so much weaker than the other forces." If this statement is true, is it still possible that there are infinite...
  45. T

    Why do we consider time as the 4th dimension?

    Time is not the 4th dimension. Well... depends on perspective. Why do people say time is the 4th dimension? I know you can say it's a dimension and there are already 3. But why not say mass is a dimension? Each point in space has a certain mass. What's the difference? Einstein said it and it...
  46. D

    Calculating the Change in Kinetic Energy During a Collision

    On a frictionless horizontal air table, puck A (with mass 0.366 kg) is moving toward puck B (with mass 0.254 kg ), which is initially at rest. After the collision, puck A has velocity 0.119 m/s to the left, and puck B has velocity 0.655 m/s to the right. What was the speed of puck A...
  47. M

    Do Black Holes Have Dimension?

    Do black holes actually have dimension (I mean size)? Thanks. :yuck:
  48. S

    Co-Exist Dimensions - Exploring Possibilities

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  49. Pythagorean

    Calculating Relative Speed in One-Dimensional Collisions

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  50. J

    What Does This Subspace Expression Mean?

    Hi everyone, I was hoping someone could help me with something. Could someone explain to me exactly what this expression means: H = {(a+b) + (a - 2b)t + bt^2 | a E R, b E R} the purpose is to find the dimension of the given subspace, which I know how to do, I have just...
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