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. R

    Can molecules exist in other dimensions?

    I took physics in high school many-many-many moons ago. Mr. Smith taught that molecules can only exist inside a three dimensional environment. Is that true?
  2. R

    The Meaning of Living in 3 Dimensions?

    What is the meaning of Living in a World having 3 Dimensions? As to the guy on the street, how is he affected by being tied to 3 dimensions? Can we make a simplified button list in language that a non scientist can understand?
  3. O

    How do i generalize this result to higher dimensions? (arc length, surface area)

    a derivation of the formula for arc length is simple enough: given a function f[x], find the length of the arc from x0 to x1. lim(x1-x0)/n=dx n->inf x1 S=^{i=n-1}_{i=0}\sum\sqrt{(x+(i+1)dx-(x+idx))^2+f(x+(i+1)dx)-f(x+dx))^2} xo...
  4. E

    Why not higher dimensions in string is timelike?

    Strings live in 9+1 world, M, 10+1 one line of criticism is string theory is unable to account for the number of large and compactified dimensions, i.e 1 (line) large, 9 curled, 2 large (sheet), 7 curled, 3 large 6 curled (our world) all the way to 9 flat or 9 curled. Is there an a priori...
  5. C

    How Do You Calculate Cam Dimensions for Optimal Rod Travel?

    Hi, Im trying to work out the dimensions of the offset on a cam for a project. I know the travel of rod c, as well as the length of the connecting rod b, but I am not sure what the lenth of dimension a should be. I know this is probably simple maths (just pythagoras?) but I need to make sure...
  6. Orion1

    How Do Planck Scale Dimensions Define Universal Limits?

    Planck energy: E_P = m_P c^2 = \sqrt{\frac{\hbar c^5}{G}} Gravitational radius: r_G = \frac{r_s}{2} = \frac{G m_P}{c^2} Gravitational radius is equivalent to Compton wavelength: r_G = \overline{\lambda}_C \frac{G m_P}{c^2} = \frac{\hbar}{m_P c} Planck force is a constant in the Einstein...
  7. Spinnor

    Surface waves on a balloon and our possible extra dimensions.

    Think about the dimensionality of a balloon with surface waves. Say these waves are of small amplitude compared with the radius of the balloon. Two coordinates label points on the balloon and a third labels radial position. Creatures who lived on the surface could make measurements that...
  8. E

    The Illusion of the 3rd Dimension: A Mathematical Perspective on Space and Time

    Holographic principle aside, I believe that there is no theoretical basis for a 3rd spatial dimension, only experiential, since we can see and measure depth, as well as height and length. From what I've read, however, all forms of depth perception require movement, or otherwise don't allow...
  9. I

    What is the construction of gamma matrices and spinors in higher dimensions?

    Dear guys, I want to understand the spinors in various dimensions and Clifford algebra. I tried to read the appendix B of Polchinski's volume II of his string theory book. But it's hard for me to follow and I stuck in the very beginning. I will try to figure out the outline and post my...
  10. B

    Do we move through higher dimensions?

    Hey there, I've just started learning quantum mechanics and I'm currently reading about gravity and higher dimensions. That is, I know so very little and would like to see if somebody could lend me some clarification . The uncertainty relation comes from the fact that matter waves in and out...
  11. D

    Different number of time dimensions

    I am layman, so I can't find an answer on my own. Suppose, on low energies space is (locally) pseudo-euclidean with the number of spatial dimensions S and time timensions T In our universe S=3 and T=1 My question: is it possible to 'adjust' equations of GR and QM/QFT to the different S...
  12. R

    Tell me how string theory works and about extra dimensions in (laymen terms)

    Iv'e scene the documentary about string theory and i just have a few questions about it.(laymen terms) : 1.How does string theory contribute to a unified field theory? 2.Is matter really made of "vibrationg strings"? 3.What does string theory actually mean or what has been the impact...
  13. Z

    Find Flux Across Portion of Sphere in 3 Ways

    Homework Statement Find the flux of field \mathbf{F}=x\mathbf{i}+y\mathbf{j}+z\mathbf{k} across the portion of the sphere x^{2}+y^{2}+z^{2}=4 in the first octant in the direction away from the origin in three ways: a. using formula for flux when sphere is a level surface b. using formula...
  14. N

    Determine the dimensions of a rectangular box, open at the top

    Homework Statement Determine the dimensions of a rectangular box, open at the top, having volume 4 m3, and requiring the least amount of material for its construction. Use the second partials test. (Hint: Take advantage of the symmetry of the problem.) Homework Equations The...
  15. Saladsamurai

    Find the Math Forming a Vector Function in 2 Dimensions

    Okay. My reason for posting this is that I need help actually formulating the 'math part' of it. I can get the right answer by 'inspection.' And from the way the book is written, I believe that is how the authors expect you to find it. But for self gratifying reasons, I wish to generalize...
  16. P

    Dimensions of Newton's Law of Gravitation and Coloumb's Law

    As we know, Newton's Law of Gravitation is \[ {\mathbf{F}} = \frac{{Gm_1 m_2 }} {{r^2 }} \] and Coulomb's law is \[ {\mathbf{F}} = \frac{{Qq_1 q_2 }} {{r^2 }} \] We know from comparing the dimensions of the first equation that G, the gravitational constant, has the dimension \[ [M^{ - 1}...
  17. S

    The effects of a solids dimensions on sound waves?

    I've been thinking, what sort of effects would changing the dimensions of a solid, (lets say a block of wood, or plank.) have on the sound waves passing through it. For example, let's say I take a block of wood, and reduce the mass and surface area (I.E cutting the ends off a plank)? or cut...
  18. B

    I'm having trouble understanding multiple dimensions up to 10

    Apologies if I've missed something fundamental - as I only have very little university Physics background (3 semesters). I've watched this old youtube video again out of curiosity: I don't think I fully understand it. This is what I have so far...
  19. K

    Work Done in Two-Dimensional Ramp Push

    Homework Statement A worker pushed the Piano weighing 93N up a ramp into a moving van, pushing horizontally, parallel to the ground. The ramp extends 4m over the ground and 3m high. The top, sloped surface of the ramp holding the piano is 5m long. The worker exerts a force of 85 N. How much...
  20. A

    How Can I Master Kinematics in Two Dimensions?

    Having diffuclty understanding the concepts, etc. I did alright for one dimension, but now I am pretty lost. I have trouble knowing what to find and how to draw everything out. (Chapter 3, Cutnell & Johnson, 7th Edition). Does anyone have any recommendations on online outlines or even youtube...
  21. D

    Pressure on sides and ends of pool, given the pools dimensions and depth

    Homework Statement A swimming pool has dimensions 34.0 m 9.0 m and a flat bottom. When the pool is filled to a depth of 2.30 m with fresh water, what is the force caused by the water on the bottom? I have the answer to this which is 6.90 x 10^6, however I cannot figure out the pressure on the...
  22. C

    Midpoint in 3 Dimensions Question (EASY)

    Homework Statement http://carlodm.com/calc/123.png My question is: Why can't we use a scalar multiple like (3/8) PQ instead of using the midpoint formula twice (to get 3/8) ?
  23. R

    Distance Formula in 3 Dimensions

    Is it possible to change: _______ distance = \/X2 + Y2 To: _______________ distance = \/X^2 + Y^2 + Z^2 And get the distance between a point in 3 dimensional space and a the point of origin, just as the first equation does in 2 dimensional space...
  24. W

    What were the velocity and direction of the glass as it fell?

    A glass is slid across a table top, goes off the edge and falls to the floor. The table is 0.860m high and the glass lands 1.53m from the edge. a)With what velocity did the glass leave the table top? b)What was the direction of the glass's velocity(degrees clockwise from the horizontal)as it...
  25. M

    Questions in [ motion in two dimensions ]

    questions in [ motion in two dimensions ] q. [ .. if you know the position vectors of a particle at two points along its path and also know the time interval during which it moved from one point to the other m can you determine the particle's instananeous velocity ? its average velocity ...
  26. P

    Motion in Two and Three Dimensions and airplane

    The airplane shown is in level flight at an altitude of 0.50 km and a speed of 150 km/h. At what distance d should it release a heavy bomb to hit the target X? -I tried using x-x0=(v0)(cos(theta))t; and then solving for t with another equation but that does not give me the correct answer...
  27. S

    MATLAB Fixing Problems Integrating Function in MATLAB

    Hey I'm having problems trying to integrate my function func1 in MATLAB. Really don't know where I am going wrong so would really appreciate if anyone could help. The code I'm using is below, thanks: Function Mfile: function [ f1 ] = func1( E, Delta, kB, Temp ) %func1: calculates...
  28. 6

    Solving Schrodinger equation in two dimensions

    Homework Statement Solve the time independent Schrodinger equation for an electron in a 2-D potential well having dimensions Lx and Ly in the x and y directions respectively.Homework Equations d^2Y/dx^2 + d^2Y/dy^2 + 2m/h^2*EY = 0The Attempt at a Solution Y(x) = A exp(jkx) + B exp(-jkx) I'm...
  29. D

    Kinematics in two dimensions problem

    A fire fighter directs a stream of water from a fire hose into the window of a burning building. The window is 20.0 m above the level of the nozzle and 60.0 m away. The hose produces a jet of water at a constant nozzle speed of v0 = 30.0 m/s. The fire fighter can control the angle θ0 that the...
  30. C

    Kinetics question in 2 dimensions

    Homework Statement A ball is hit by a golfer. The angle is 28 degrees, the velocity of the projectile is 16.0, the distance is 16.8m on horizontal. What is the velocity before impact on the ground of the ball? Homework Equations The Attempt at a Solution
  31. J

    Derivation of formula using dimensions

    Can we derive the equation , F = (Gm1m2) / r2 using dimensional analysis?
  32. C

    Black Hole Dimensions: Reversing the Universe's Expansion

    In terms of physical dimensional size, what are the measurements a black hole must fit in order for it to actually reverse the expansion of the universe and cause a total suction of the space-time fabric that constitutes our universe, in its current position? I will appreciate a profound...
  33. S

    Calculating Time of Impact for Released Ballast Bag in 2D Kinematics

    Homework Statement A hot-air balloon is rising straight up with a speed of 2.4 m/s. A ballast bag is released from rest relative to the balloon when it is 9.6 m above the ground. How much time elapses before the ballast bag hits the ground known data y direction vo = 2.4 m/s a =...
  34. P

    Euqation of kinematics in two dimensions

    Fans claim that Michael Jordan is able to jump and remain in the air for two full seconds from launch to landing. Evaluate this claim by calculating the maxium height that such a jump would attain. For comaprsion, Jordan's maximum jump height has been estimate at about one meter. Y=1meter...
  35. P

    Euquations of kinematics in two dimensions

    A golfer imparts a speed fo 26.0m/s to a ball, and it travels the maximum possible distance before landing on the green. The tee and the green are at the same elevation. A.) How much time does the ball spend in the air? B.) What is the longest "Hole in one" that the golfer can make, if the ball...
  36. C

    Four Dimensions: The Key to Understanding Existence

    There are 'four' experimentally proven dimensions. Anything and everything must be defined by 'four' dimensions. It doesn't make sense to me to say "An Object exists in two dimensional space" or "Three dimensional." To mean there is one dimension, what everything exists in, defined by...
  37. G

    Entropy and Energy in Higher Dimensions

    How do we know that energy behaves the same way in higher dimensions as it does for 3-dimensions? With a higher dimensional freedom, it might actually behave differently - if, for example, time were a flexible degree of freedom, then descriptions, such as entropy, wouldn't necessarily be...
  38. C

    Kinematics in two dimensions - question?

    I'm having problems with this problem. Can anyone help me? A space vehicle is coasting at a constant velocity of 21.4 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.350 m/s2 in...
  39. I

    What are the dimensions of abs(b_{n})^2 and abs(b(k))^2 in particle functions?

    Homework Statement If an arbitrary intial state function for a particle in a box is expanded in the discrete series of eigenstates of the Hamiltonian relevant to the box configuration, one obtains: \psi(x,0) = \Sigma^{\infty}_{n=1}b_{n}(0)\varphi_{n}(x) If the particle is free, we obtain...
  40. J

    Sphere rolling inside cylinder - 3 dimensions

    Homework Statement A sphere of radius r and mass m rolls without slipping inside a hollow cylinder of radius R. z direction goes along axis of cylinder. Determine the Lagrangian with motion in the z direction included Homework Equations I let θ be the angle of the sphere rotation...
  41. W

    Why do we need compactified dimensions?

    I know that the compactified additional dimensions is the standart explanation, but the way I have thought of this is: The reason we can't see these dimensions, is that light fotons are bound to the 3rd D, and can't escape. Just like waves at the ocean can't escape its 2D surface. and neither...
  42. J

    Threading #6-32 UNC Hole in Plexiglass - DIY Guide

    Probably a stupid question but... I have a device with a bolt that is designated #6-32 UNC. I need to drill a hole in a surface to for this bolt to fit into. How big should this hole be? If the material I am going to be threading the bolt into is plexiglass do I need to thread the hole I...
  43. G

    Secrets of the Microwave Oven: Grid Dimensions & Polar Molecules

    Homework Statement Microwave oven I. The glass window isn't important to the microwave oven's operation, but the metal grid associated with that window certainly is. The grid forms the sixth side of the metal box that traps the microwaves so they cook food effectively. What is the approximate...
  44. W

    Heat Transfer shareware for 2 Dimensions?

    Greetings, I'm trying to design a system that creates a thermal gradient in 2 dimensions through several layers of very different material (copper, acrylic, and ice). I was wondering if there's some cheap software available or even some kind of shareware out there that could give me at least...
  45. M

    What is Compactified Extra Dimensions?

    Hi, I have a question about extra dimensions. I don't understand what means that a dimension is compactified. Thanks a lot! Sorry it's the wrong forum. It belongs to Beyond the Standard Model , but I don't know how to remove it!
  46. K

    Electromagnetism=gravity in higher dimensions

    I recently read an article(http://www.newscientist.com/article/mg20327231.900-beyond-space-and-time-5d--into-the-unseen.html) that said that gravity in the fifth dimension could be electromagnetism, but wasn't his math flawed? I seem to recall there being something wrong with this idea.
  47. D

    A rectangular block has dimensions 2.9cm x 3.5cm x 10.0cm. The mass of

    A rectangular block has dimensions 2.9cm x 3.5cm x 10.0cm. The mass of the block is 615.0 g. What are the volume and density of the block? how do you do it?
  48. W

    Can Gravity Escape Higher Dimensions in String Theory?

    according to string theory, gravity got the ability to escape the D-brane of witch all matter is bound. The reason is that the boson carrying the gravity is a loop-string, with no open ends linking to the brane.. this theory should explain why the gravity is so much weaker than the other forces...
  49. J

    The Mystery of dS Space: Exploring the Role of the Extra Dimension

    I am simply trying to understand why dS space has a signature (4+1) ? Good old familiar Minkowski space is of course, (3+1), crystal clear. What is the role of the extra spatial dimension in dS ? Why should the manifold be 5-D ?
  50. P

    Exploring the Possibilities of 5-Dimensional Objects and their Surfaces

    Can there be a place(?) where only 5 dimesional object are allowed? Or would there always be the need for a 4 dimensional surface of the 5 dimensional obect? If you'll always need to be able to subtract a dimension (the edge of a 2d plane is a 1d line and the end of a 1d line is a 0d...
Back
Top