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.

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

    Inelastic Collision in Two Dimensions

    Homework Statement A 1300-kg car collides with a 15,000-kg truck at an intersection and they couple together and move off as one leaving a skid mark 5m long that makes an angle of 30.0° with the original direction of the car. If μk = 0.700, find the initial velocities of the car and truck...
  2. C

    If energy/matter deforms spacetime in three dimensions

    If energy/matter deforms spacetime in three dimensions... Then why do we get galaxies in (relatively) flat discs and black holes that emit radiation in a single plane?
  3. J

    Kinematics 2 dimensions problem, golf ball being hit

    A golf ball mass of 4.7 x 10-2 kg is hit by Tiger Woods and drops exactly into a hole 100 meters away. It is observed that the angle between the initial velocity vector and the horizontal plane is 30 degrees. What is the magnitude of the initial velocity? Isn't the problem missing...
  4. C

    Need quick answer on spatial dimensions

    I have just a quick question I was wondering about and I was wondering could someone answer it here. Is it true that for example the third dimension is composed of an infinite number of 2 dimensional planes on top of each other which give rise to width, the third dimension? If this is true...
  5. C

    Question on higher spatial dimensions

    I have just a quick question I was wondering about and I was wondering could someone answer it here. Is it true that for example the third dimension is composed of an infinite number of 2 dimensional planes on top of each other which give rise to width, the third dimension? If this is true...
  6. K

    What must the Dimensions of G be for this equation to be dimensionally correct?

    Homework Statement "An object from the surface of the Earth with the escape speed ve can move infinitely far from the Earth. The escape speed is independent of the mass that is trying to escape and only depends on G, the gravitational constant, ME the mass of the Earth, and RE the radius of...
  7. F

    Kinematics in Two or Three Dimensions

    Homework Statement At t = 0 a batter hits a baseball with an initial speed of 29 m/s at a 55° angle to the horizontal. An outfilder is 85 m from the batter at t = 0 and, as seen from home plate, the line of sight to the outfilder makes a horizontal angle of 22° with the plane in which the ball...
  8. T

    Statics of body in two dimensions

    Homework Statement Homework Equations A 50 lb force is applied to a corner plate as shown. Determine an equivalent system consisting of a 150 lb force at B and another force at A. The Attempt at a Solution There is an algebraic solution to the problem, but I was wondering if it...
  9. F

    How Does Table Height Affect Initial Velocity Calculation in Physics?

    Homework Statement I am trying to calculate the (Vo) for a ramp length from a horizontal decline marked at 20 cm. The ramp on top of a table has an angle of 41 degrees. I performed 3 trials releasing a ball bearing at the 20cm mark and averaged 53.3 . The table height is 87.3 cm. Isn't Vo...
  10. M

    Kinematics in two dimensions lab question

    Homework Statement Using your understanding of projectile motion along with some background research on video analysis, devise a way to find the initial velocity of the tennis ball in the video just as it enters the bottom left of the screen. There is some important information for you to...
  11. N

    What are the mathematical concepts used to describe angles in three dimensions?

    We usually describe angles in two dimensions (x and y plane). What is the mathematics behind three dimensions?
  12. J

    Height of an ellipse above the plane in three dimensions (z parameter)

    Homework Statement What is the expression for z (the height above the xy-plane) in terms of r,f,w,i. r = the distance f = the angle between the semi-major axis and the r vector w = the angle that the semi-major axis makes with the y-axis i = the angle that the plane of the ellipse makes...
  13. X

    Massive Scalar Field in 2+1 Dimensions

    Homework Statement We wish to find, in 2+1 dimensions, the analogue of E = - \frac{1}{4\pi r} e^{-mr} found in 3+1 dimensions. Here r is the spatial distance between two stationary disturbances in the field. Homework Equations In 3+1 we start from E = - \int \frac{ d^3 k }{(2\pi)^3}...
  14. N

    Describing vectors in n dimensions

    Recall that A can be broken up into its components x,y, and z. Can You simply add more components to describe any number of dimensions. Where n would be nth dimension? A=A_x+ A_y+A_z+⋯A_n
  15. M

    Capacitance of a capacitor with dielectric of variable dimensions and constant volume

    Homework Statement Homework Equations \int\vec{E}\cdot\vec{dA}=\frac{Q_{enc}}{\epsilon_{0}} \int\vec{E}\cdot\vec{dA}=\frac{Q_{enc}}{k\epsilon_{0}} V=\int\vec{E}\cdot\vec{dS} C=\frac{q}{V} C_{eq}=C_{1}+C_{2}+... \frac{1}{C_{eq}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+... The Attempt at...
  16. J

    Re: Piezoelectric dimensions problem in energy harvesting

    hi I am doing project on piezoelectric energy harvesting which is a cantilever structure using COMSOL. I have some doubts related to my project. I designed cantilever structure having three layers substrate (SiC), piezo (ZnO) and electrode (Al). My doubt is that when piezoelectric layer...
  17. A

    Maximum Initial Velocity of a Tennis Ball: Solving for the Optimal Launch Speed

    Hi there all, I'm new to this forum and I really need some help. The question is described as follows: Estimate the maximum "initial velocity" that you can achieve with a regular tennis ball. Presumably there are no variables, nor are there any equations involved. I think that an...
  18. P

    How Does Playing Snake in 4 Spatial Dimensions Work?

    Hi everybody, I've a started a little a game, it is based on the nokia game snake, where you have to guide the snake and eat the food. I wrote a little script in python, and a C++ version of the game but in 4 spatial dimension. The snake moves through a euclidean 4 space. what do you...
  19. W

    Taylor expansion, of gradient of a function, in multiple dimensions

    Hello all, I understand that the taylor expansion for a multidimensional function can be written as f(\overline{X} + \overline{P}) = f(\overline{X}) + \nabla f(\overline{X}+t\overline{P})(\overline{P}) where t is on (0,1). Although I haven't seen that form before, it makes sense...
  20. L

    Exploring the Dimensions of Tension and Linear Mass Density

    What are the dimensions of tension? What are the dimensions of linear mass density? Thank you!
  21. L

    Find the dimensions of surface tension

    I would really appreciate some help with this! h= (L) r=(L) p=(ML-3) g=(LT-2) I just don't know what to do with the directly proportional sign. Should I isolate the surface tension before or after adding the constant?
  22. F

    Motion in two or three dimensions

    Hi. I am lost in this problem. Could someone tell me what to do. How to start with the problem?
  23. F

    Relative motion in two dimensions question

    Ship A is located at 4 km north and 2.5 km east of ship B. Ship A has a velocity of 22 km/h toward the south, and ship B has a velocity of 40 km/h in a direction 37 degrees north of east. (a) What is the velocity of A relative to B in unit-vector notation with i toward the east? (b) Write an...
  24. I

    Can 12-Dimensional Tic-Tac-Toe Help Visualize Higher Dimensions?

    Hi, I've developed a game, or some may say tool, that aids in the conceptualization and visualization of movement in the higher dimensions. It is 12 dimensional tic-tac-toe. By competing with an opponent to connect points in 12 dimensions, one can truly get a grasp for the arbitrariness of...
  25. A

    5D Space,Higher Dimensions etc.

    Let us consider the metric given by the following line element: {ds}^{2}{=}{dr}^{2}{+}{r}^{2}{(}{d}{\theta}^{2}{+}{Sin}^{2}{(}{\theta}{)}{d}{\phi}^{2}{)} For a particular value of r we have two independent coordinates in the embedded surface--and the surface has been embedded in a 3D space.For...
  26. T

    Lorentz contraction in other dimensions?

    Hi guys, this is my first post/thread, so I'd like to start with an easy one:rolleyes: I've searched the web and I wasn't able to find a satisfying proof of the fact that Lorentz contraction is NOT applied to the dimensions, that are not parallel to the direction of motion (e.g...
  27. S

    Bravais Lattice in Two Dimensions

    In the book Applied Physics by P.K.Mittal, on page#25 under the heading of "Bravais lattice in two dimensions", a paragraph says, "The number of point groups in two dimensions is 10." My 1st question is, Then how many in three dimensions? Paragraph further says, "10 groups in two...
  28. C

    Dimensions of cone with smallest volume that can hold a cylinder

    Homework Statement A cylinder of height 45mm and radius 12mm is placed inside a circular cone. What are the dimensions of the cone with the smallest volume to enclose this cylinder Homework Equations v=1/3(pi)r^2h v=(pi)r^2h SA=2(pi)rh The Attempt at a Solution I substuted values...
  29. T

    Proof for the Impossibility of Higher and Lower Dimensions

    Introduction The premise that our universe might have more spatial dimensions than the three that are immediately apparent is so widespread and popular that it is nearly accepted already as a fact despite the absence of evidence. This is primarily the result of two separate influences: the...
  30. N

    What is the study of higher dimensions?

    What is the study of higher dimensions called? What I'm referring to are hyper cubes and such. I finished basic math this past year (calc123, ode and linear alg) and I really want to learn the calculus of higher dimensions. Does a field like this exist?
  31. L

    Infinite dimensions and matrices

    Homework Statement Find 2 more orthonormal polynomials on the interval [-2,1] up to degree 2 given that the first polynomial p(x) = 1/√3. ( Note: Take the highest coefficient to be positive and enter your answer as a decimal.) Homework Equations This is a web assign equation so the answer...
  32. S

    Why is the time dimension different from the 3 space dimensions

    General relativity states that our universe is four dimensional curved space so time dimension is not separated from space dimensions .Why then is the time dimension different from the 3 space dimensions ? and why there must be 3 space dimensions and not 4 for example ?
  33. M

    Kaluza-Klein theories in twelve dimensions and F-theory

    "Kaluza-Klein theories in twelve dimensions" ... and F-theory This is a separate thread to discuss another idea by arivero, originally https://www.physicsforums.com/showthread.php?t=485247&page=4#63". Some references: http://www.sciencedirect.com/science/article/pii/0550321385902329" )...
  34. N

    What do dimensions physically signifies?how does they affect the

    what do dimensions physically signifies? how does they affect the space/time?
  35. H

    Exploring Higher Dimensions: Beyond Our Understanding?

    https://www.youtube.com/watch?v=http://www.youtube.com/watch?v=ySBaYMESb8o How can they predict anything after dimension 7? Especially the part where they go from dimension 8 to 9. Isn't everything in that dimension supposed to be in-explainable by the our science and minds? And isn't...
  36. B

    Expanding Mathematica code from 2 dimensions

    I have this mathematica code to solve a variation of the 2 Dimensional Poisson's equation using the finite difference method. xo = .5; yo = .5; \[Sigma] = .05; q = 1; Gen[x_, y_] := -q*E^-((((x - xo)^2) + ((y - yo)^2))/(2*\[Sigma]^2)); GridNum = 300; Hstep = N[1/(GridNum + 1)]; GridPts...
  37. W

    Do Partial Spatial Dimensions Exist?

    So I'm sure everyone here knows of the basic spatial dimensions. 1D is a line, 2D a plane and 3D a cube. There is even a 4th dimension (theoretical), the tesseract. And an infinite number of dimensions beyond, represented by various hypercubes. Finding the space taken up by one of these objects...
  38. D

    Calculating Square Tubing Dimensions for Vertical Bicycle Support

    I would like to know which calculations to use to determine the dimensions, including the thickness of square tubing that needs to carry a load of 6 bicycles each weighing 18kg. The bicycles are vertically suspended from the tubing and the support is in the middle of the tubing so the ends are free.
  39. S

    Visualizing seven extra dimensions

    Hi, I am a sculptor working with glass. I have come to this forum for some information. Several years ago I read an article on sting/M-theory that gave a description of one of the possible shapes the the 7 compact extra dimensions of m-theory. I have been unable to find the article again. I...
  40. F

    What is the relationship between horizontal and vertical radii in a bent pipe?

    I have a question, and I hope I can word it correctly. Say I have a round pipe of length 5 feet (actually, the length is irrelevant). I want to bend it at a certain radius in the horizontal direction, and also a certain radius in the vertical direction. Let's say I bend it at 20' horizontal...
  41. L

    Can someone explain to me exactly what is meant by vanishing dimensions theory?

    I really like it, but haven't seen any good, simple descriptions of it! Is there any place to get just the overall gist of it?
  42. O

    Time and physicality of dimensions

    Is it correct to say that the three space dimensions are no more physically (as in materially) real than the time dimension, but that only the mass that exists in the dimensions are real in a material sense? I have a suspicion that why som people insist that time (and spacetime) does not exist...
  43. G

    Motion of object in 2 dimensions

    A ball is kicked from 12 m high traveling horizontally at 1.3 m/s. How would the horizontal motion affect the vertical motion and why?
  44. T

    Exploring Symmetry in Extra Dimensions: SO(n,1) & SO(3,1)xG

    Hi how, in my master project I am working on extra dimensions and I am asking my self why is it common to start most of the theories with a space time symmetry given by SO(n,1) (n>4) and then compactify the obtained spectrum to SO(3,1)xG (where G is an abitrary symmetry group). Because...
  45. H

    Dimensions of temperature and charge in terms of M, L and T

    "Most physicists do not recognize temperature, Θ, as a fundamental dimension of physical quantity since it essentially expresses the energy per particle per degree of freedom, which can be expressed in terms of energy (or mass, length, and time). Still others do not recognize electric charge, Q...
  46. Spinnor

    Could hidden dimensions help hidden variable theories ?

    Could hidden dimensions help "hidden variable theories"? Could extra unobserved dimensions be of use in finding a hidden variable type theory that also satisfied Quantum Theory? Thanks for any help!
  47. S

    Matrix dimensions are not matching after differentiation

    I'm doing some work with neural networks lately and I'm having trouble with this seemingly simple equation. The equation describing the network is: y = \psi(W3 x \psi(W2 x \psi(W1 x I))) Where: y (scalar) is the output value W1 (2x2 matrix) are the 1st layer weights W2 (2x2 matrix) are...
  48. Y

    Questions about light speed, time, and dimensions.

    I am not a scientist just an observer and enthusiast. We have 3 spatial dimensions and one dimension of time. What I have been wondering is... could time have more than one dimension? I mean we percieve time as a continuous line, but can time move in other ways that we cannot percieve, like...
  49. K

    Calculating the dimensions of an arc

    Dear all, I feel this should be a simple problem but I can't solve it. Could you give me a hand? Imagine if an arc is bounded by a rectangle of dimensions width and height. The arc starts in the bottom left corner of the rectangle, and ends in the bottom right corner. The apex of the...
  50. T

    Electrodynamics in two space dimensions :-(

    Hi all, I've got this problem (which is attached as q1.jpg). I've tried to solve it, but I'm stuck... my solution is also attached (my_sol1.jpg). PLS help me :-( Thnx TED
Back
Top