Dimensions Definition and 1000 Threads

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.

View More On Wikipedia.org
Recent contents Top users
  1. Daaavde

    Is Dimension 3 Enough to Prove Isomorphism Between Spaces?

    Is it correct to state that if a space E has dimension 3 then: E = ℝ^{3} and that the two spaces are isomorph?
  2. P

    What is the net force acting on the log after 10 seconds?

    Homework Statement Two tugboats are pulling a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s? http://imgur.com/GS7Y80x Homework Equations c^2=a^2 + b^2 -2ab cosC sin A/ a= sin...
  3. B

    Finding min. value of dimensions for a tank of water

    Hello Homework Statement An open tank is constructed with a square base and vertical sides to hold 32m3 of water. Find dimensions of the tank if the area of the sheet metal used to make it is to have a minimum value. Homework Equations The Attempt at a Solution I'm not...
  4. R

    How to Find Density of States for Quantum Gas in D Dimensions?

    Homework Statement Find the density of states g(ε) for an ideal quantum gas of spinless particles in dimension d with dispersion relation  ε= α|p|s , where ε is the energy and p is the momentum of a particle. The gas is confined to a large box of side L (so V = Ld) with periodic boundary...
  5. E

    Is Phi^3 Theory in Five Dimensions Supposed to Be Finite?

    OK, I think I am missing something very basic... When regularizing phi^3 theory in six dimensions, Srednicki comes to eq 14.30, which shows that the 1-loop contribution to the propagator diverges (the gamma function has a pole). This is good. OK. Now let d=5 (or epsilon=1). Actually, go...
  6. A

    Dimensions - how many are there in universe?

    dimensions -- how many are there in universe? how many dimensions are there in universe and what are they ?
  7. StevieTNZ

    Number of Dimensions + Laws of Physics

    Can the laws of physics work with any number of dimensions (whether they be space or time)? That's what Lisa Randall claims, but am seeking clarity. If so, does that mean Quantum Mechanics will still predict the same results in 5 or 6 dimensional universes, and the equations will stay the...
  8. M

    Dimensions of radiation detector and range of secondary particles

    Hi All, Just reading up on methods of neutron detection and something struck me. Generally these types of detectors are manufactured small enough so the the ranges of the charged particles (usually tritium and alpha) are smaller than the dimensions (so around 100microns or so). This means...
  9. G

    Why Do SO(n) & SU(n) Have Different Dimensions Despite Same Constraint?

    Qhy does SO(n) have the same number of dimensions of O(n), whereas SU(n) reduces the dimensions of U(n)? Isn't the constraint the same for both cases, i.e. detM=1?
  10. Avatrin

    Algebra and Calculus in three dimensions

    Hi I have realized that I am horrible at setting up integrals in three dimensions when working with Coulomb's law (F = k q*∫r-2dq ). I don't have the vaguest idea how I can solve this using it and the superposition principle: I am not asking for a solution to this exercise. I want a good...
  11. Z

    Dimensions and Dimensional analysis question

    In this formula, E = 1/2 mv² 1/2 is not considered as it does not have any dimension. But then does it not affect the formula. Why? Explain! Please
  12. N

    Determining dimensions of a rectangle

    Homework Statement A box has a length that is 13cm longer than its width, and the volume of the box is 60cm^3. Determine the dimensions of the box. Homework Equations V = lwh l = 13cm > w h = ? The Attempt at a Solution Since V = lwh, 60cm^3 = lwh and, l = 13cm > w w...
  13. L

    Is another form of time one of the extra dimensions?

    Sorry. I know I must sound like a hick. Time is ... the 4th dimension of our conventional reference? If so, are one or more of the other dimensions posited by String Theory considered possibly to be an additional time dimension(s)?
  14. O

    Dimensions related to Planck's constant H

    Consider a system where the three fundamentally important quantities are the speed of light C with dimensions (L)/(T), Planck's constant H with dimensions (M)(L)^2/(T), and the mass of the proton M sub p with dimension (M). a) What combination of ratios and/or products of C, H, and M sub p will...
  15. N

    Thermodynamics - Calculate power and dimensions of piping

    Homework Statement 500 kg/hr of steam drives a turbine. The steam enters the turbine at 60 bara and 500C at a linear velocity of 5.0 m/s. After driving a set of turbine wheels to generate shaft power, the steam exhausts from a pipe that is 10 m below the entrance pipe at 35.0 m/s and at 2.5...
  16. P

    Four features from three dimensions?

    Hi math fans, Only me, I have been asked to do the seemingly impossible and find away of distinguishing four signals from three dimensional space. Any ideas guys - left me stumped. Thanks for thinking about it anyway Cheers Duane
  17. K

    Unfurling the string dimensions

    According to string theory there are an extra 7 spatial dimensions curled up at every point in space. They are so small(Planck length) that nothing can move through them and are completely undetectable. My question is this: Does string theory allow for these dimensions to uncurl and become...
  18. C

    Litterature on small or compact dimensions?

    Litterature on "small" or "compact" dimensions? Hi! I'm reading some Kaluza-Klein theory which is an extension of normal 4D GR to a 5D spacetime in which the fifth dimension is a "small" or "compact" extra spatial dimension. I've found loads of literature on the differential geometry of...
  19. T

    Acceleration in Two Dimensions (Vector)

    Homework Statement A bird flies from Lesser Slave Lake in northern Alberta to Dore Lake in northern Saskatchewan. The birds displacement is 800.0 km [E 7.5deg S]. The bird then flies from Dore Lake to Big Quill Lake, Saskatchewan. This displacement is 400.0 km [E 51deg S]. The total time of...
  20. C

    Angle between a vector and a unit vectors with 3 dimensions.

    Find a two unit vectors that make the angle \pi/3 with the vector \vec{v} = \vec{i} + 2\vec{j} + 3\vec{k}. "That isn't asking much since there are apparently infinite such vectors" - Prof. I get as far as to say that \pi/3 = arccos( 1/2 ) and that \frac{v \bullet w}{|v||w|} = 1/2 but from...
  21. W

    Finding velocity equation for object moving in 2 dimensions

    A fkdkdkel
  22. E

    Dynamics in Two Dimensions Question

    Homework Statement During baseball practice, you go up into the bleachers to retrieve a ball. You throw the ball back into the playing field at an angle of 42° above the horizontal, giving it an initial velocity of 15 m/s. If the ball is 5.3 m above the level of the playing field when you...
  23. C

    Spatial dimensions of our universe

    On the page 17 of this article by Max Tegmark http://arxiv.org/pdf/gr-qc/9704009v2.pdf, in figure 7, it has been argued that why spatial dimensions other than 3, is not possible for our universe. But in string theory, people are talking about 10, 11 or 26 spatial dimensions (even if these...
  24. K

    System of Linear Equations to Resolve Room Dimensions

    Homework Statement Twelve equal rectangular ceiling panels are placed in a four long by three wide grid. Each panel is 150mm longer than it is wide. Between the panels runs an edge/middle strip which totals 40.0m in total length. (This runs round the whole perimeter and between each panel)...
  25. P

    Local Electrodynamics in higher dimensions?

    Local Electrodynamics in higher dimensions?? So I am an unexperienced undergrad but the other day I had a few thoughts which are most likely crazy. I'm just wondering why they don't work. And whether the questions I'm asking are answered elsewhere. So I've heard: (i) Maxwell's...
  26. H

    Does String Theory tell us the size of Extra Dimensions.

    Does the math in string theory tell us anything about the size of any of the extra dimensions?
  27. H

    Is Quantum World weird because we can 'see' higher dimensions?

    Let me try to explain. If I take a reel of movie film, I can unwrap it see different frames simultaneously. How ever if I were "trapped" in the movie I could only experience one frame at a time. Now this example is not a direct proposition I am making. It''s just to imagine a higher...
  28. S

    Inelastic collisions in 2 dimensions

    I am unsure how to proceed with this problem because it is asking for the final velocity of one of the two objects given the initial velocities. This is an inelastic collision not a completely inelastic collision, which means the two objects do not stick together. The book makes a distinction...
  29. S

    Energy conservation in two dimensions

    In an experiment, one of the forces exerted on a proton is F = −αx^2i , where α = 14.4 N/m2. (a) How much work does F do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.5 m)? (b) Along the straight-line path from the point (0.09 m, 0) to...
  30. Z

    Weyl tensor in 2 dimensions- confused

    hello, The Weyl tensor is: http://ars.els-cdn.com/content/image/1-s2.0-S0550321305002828-si53.gif In 2 dimensions , the Riemann tensor is (see MTW ex 14.2): Rabcd = K( gacgbd - gadgbc ) [R] Now the Weyl tensor must vanish in 2 dimensions. However, working with the g g = [-1 0 0...
  31. M

    Questions About Dimensions & Time

    So I watching this video on dimensions.. and I have a few questions: 1. How many dimensions are there? (that are proven with hard evidence) 2. The video was talking about 4-Dimensions - is it pretty much the same thing as 3-Dimension + time?
  32. B

    Are small extra space-time dimensions represented correctly?

    Are "small" extra space-time dimensions represented correctly? This is my first post, I searched briefly but I apologize if this is a commonly covered topic! The following is written in the spirit of the "aether" -- that, being an overcomplication with no evidence. One of my biggest...
  33. B

    Fundamental theorem in 2 dimensions.

    Hello I have heard that Greens, Stokes and the Divergence theorem is the equivalent of the fundamental theorem in multiple dimensions. But is there some way to show the result under: if F(x,y) = \int_{-\infty}^x\int_{-\infty}^yf(x^{*},y^{*})dx^{*}dy^{*} this implies that...
  34. K

    4+ spatial dimensions and how to manage them

    Basically, I'm writing a story that involves beings of 5 spatial dimensions visiting Earth. And when I say "writing" I mean "putting thoughts down on paper as they come to me" or almost that, i.e. not much thought has gone into world-building. Mostly 5-dimensionality manifests in crazy...
  35. S

    Minimal Dimensions for Maximum Bending Moment

    Hi Please can someone help me calculate the minimal thickness and width that will resist bending in each of the aluminium beams that are fixed on one end and support a 0.0013734 Newton load on the other. The axis passes through the center of the octagonal shape and goes into the page...
  36. D

    Equation of circle in 3 dimensions

    Homework Statement Hi, I am trying to find the general formula of a circle in 3D Let's consider a sphere centred at (x1,0,0),with radius x1 It's equation is (x-x1)^2 + y^2 + z^2 = (x1)^2 If there is a plane x = x1 intersects with the sphere A equation of a circle is formed,which is y^2 +...
  37. A

    If two units have the same dimensions are they always inequivalent?

    If two units have the same dimensions are they always inequivalent? I was thinking, would doing dimensional analysis on units prove they are equivalent or could they have the same units but not be equivalent.
  38. W

    Troubleshooting Vector Angles in Three Dimensions

    ok so I am not sure how else to do this problem, my answers look similar to those in the book. where they have β=52.5 \alpha=121 \gamma=53.1, I feel like the book is wrong because i don't see any other way to solve this problem...
  39. P

    Laplace's equation in two dimensions.

    Hi all, Had a doubt regarding Laplace's equation. In many textbooks, the general solution to the two dimensional Laplace's equation is mentioned as: \Phi(\rho,\phi) = A_{0} + B_{0}ln(\rho) + \sum_{n=1}^{\infty}\rho^n(A_ncos(n\phi) + B_n sin(n\phi)) + \sum_{n=1}^{\infty}\rho^{-n}(C_n cos(n\phi)...
  40. S

    Do we live in 3 or 4 dimensions?

    pleese don't critical on my little knowledge of this. a few of us have bull sessions sometimes and my cousin points front side up and says we live in 3 dimencions but the whole universe is 4 dimencions. this other guy always says my cousin is full of bull and einstine just used them for...
  41. V

    Torque has dimensions of energy

    I just noticed that torque has dimensions of energy! What does that mean?
  42. O

    Lagrange Multiplier-to find out the dimensions when metal used min.

    Lagrange Multiplier----to find out the dimensions when metal used min. Homework Statement I have a rectangular tank with a capacity of 1.0m^3. The tank is closed and the cover is made of metal half as thick as the sides and base. Find the dimensions of the tank for the total amount of metal...
  43. S

    Why do we consider higher dimensional operators in the search for new physics?

    I am confuse about the dimension of an operator? Why we need an operator of Dim six or greater for new physics?
  44. C

    Could absolute motion exist in higher dimensions, if they exist?

    If the universe follows a 3-torus or finite unbounded shape, or we are situated on the surface of a 4D sphere, then the 'centre' if the universe will exist. If one could locate the position of this origin in 4D space, and remain stationary with respect to it, then would that object be at...
  45. M

    What exactly is a vector in and 5-D and more dimensions?

    I'm having a hard time grasping the concept of a vector geometrically. A vector in $$ℝ^2$$ is a line going in the direction specified from the terms. A vector in $$ℝ^3$$ is similary just a line going in the direction specified by the terms. But what exactly is a vector in $$ℝ^n$$ where n is...
  46. T

    Dimensions for a Steam Piston Valve

    Hello, I'm Nate, and I'm looking to build a compressed-air engine. I'm using a pneumatic cylinder with a 3" bore and a 12" stroke. That was simple enough to find. What hasn't been simple to find is a manual valve large enough to actuate it. I've found small 5-way valves on ebay and amazon, but...
  47. K

    Solving for Stress and Strain in Three Dimensions

    Homework Statement Knowing that the stress and strain for an isotropic media can be related with the following expressions: \sigma_{xx} = (\lambda + 2\mu)\varepsilon_{xx} + \lambda\varepsilon_{yy} + \lambda\varepsilon_{zz} \sigma_{yy} = \lambda\varepsilon_{xx} + (\lambda +...
  48. C

    Finding unit cell dimensions of iron or copper

    Homework Statement The research notes from an x-ray diffraction experiment were damaged and information was lost. The wavelength of the x-rays used in the experiment, and measurements of the three smallest Bragg angles (θ) from the sample were all that remained: they were 0.71Å, 10.1°, 14.4°...
  49. S

    Quadratic equations: Perimeter and Area fencing dimensions

    Homework Statement The following enclosure is built using 280 m of fencing. If the enclosure has a total area of 2800 m2, what are the dimensions to the nearest tenth? Homework Equations x = \frac{-b ± \sqrt{b^{2}-4ac}}{2a} The Attempt at a Solution Please note that the 3/2w and 5/2w...
  50. S

    Are grand unified theories the solution to the problem of multiple fields?

    A lot of below might be a question of semantics however it helps to understand better, I am a novice: 1. What's the difference between a field and a dimension? A field is present at all points in time and space, ...so is a dimension. why don't we call/label a field as a dimension? 2. or...
Back
Top