# What is 3 dimensions: Definition and 68 Discussions

Three-dimensional space (also: 3D space, 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point). This is the informal meaning of the term dimension.
In mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called three-dimensional Euclidean space (or simply Euclidean space when the context is clear). It is commonly represented by the symbol ℝ3. This serves as a three-parameter model of the physical universe (that is, the spatial part, without considering time), in which all known matter exists. While this space remains the most compelling and useful way to model the world as it is experienced, it is only one example of a large variety of spaces in three dimensions called 3-manifolds. In this classical example, when the three values refer to measurements in different directions (coordinates), any three directions can be chosen, provided that vectors in these directions do not all lie in the same 2-space (plane). Furthermore, in this case, these three values can be labeled by any combination of three chosen from the terms width, height, depth, and length.

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1. ### B Proof Pertaining to Possible Paths Through 3 Dimensions

I'll try to phrase this as clearly as possible but my use of terminology might need to be refined. That may be what ultimately comes of this thread, but hopefully the question as I phrase it will make enough sense. I'm not necessarily asking that a proof be provided, rather, I am interested to...
2. ### Magnetic field in 3 dimensions

The problem is as above, My attempt is as below but there is lot of effort in terms of imagining and not very confident, Required the magnetic field on the y-axis let us say point P. The magnetic field due to the x-axis wire is out of the paper at P with the values as R=2.0m, i =30A. B1 =...
3. ### Solving Electromagnetism problems in 3 dimensions

i am able to understand problems and solve electromagnetism problems, if the currents are given to be flowing in wires and circle loops in the xy axis. But if they provide similar problems in z axis i am finding it difficult to imagine and do the calculations. My question is any simple concepts...
4. ### A One Loop Correction to a 4 pt. function in 3 dimensions

If I have a Lagrangian of the form \mathcal{L}=-\frac{1}{2} (\partial \phi)^2 - \frac{1}{2} m^2 \phi^2 - \frac{\lambda}{3!} \phi^6, in 3 dimensions, what is the one-loop correction to the 4-point function? Am I correct in thinking that the following Feynman diagram is the representation of the...
5. ### Green's Theorem in 3 Dimensions for non-conservative field

Homework Statement C is the directed curve forming the triangle (0, 0, 0) to (0, 1, 1) to (1, 1, 1) to (0, 0, 0). Let F=(x,xy,xz) Find ∫F·ds. Homework EquationsThe Attempt at a Solution My intial instinct was to check if it was conservative. Upon calculating: ∇xF=(0,-z,y) I concluded that...
6. ### Normalization of the Fourier transform

Homework Statement The Fourier transfrom of the wave function is given by $$\Phi(p) = \frac{N}{(1+\frac{a_0^2p^2}{\hbar^2})^2}$$ where ##p:=|\vec{p}|## in 3 dimensions. Find N, choosing N to be a positive real number. Homework Equations $$\int d^3\vec{p}|\Phi(p)|^2=1$$ , over all p in the 3...
7. ### Magnetic field in 3 dimensions

Homework Statement One component of a magnetic field has a magnitude of 0.0431 T and points along the +x axis, while the other component has a magnitude of 0.0686 T and points along the -y axis. A particle carrying a charge of +1.70 × 10-5 C is moving along the +z axis at a speed of 4.24 × 103...
8. ### I Projection down 3 dimensions for aperiodic tiling/quasicrystal

I once took notes from a website, and now I cannot find the reference anymore, so I am attempting to reconstruct it, and am sure that I have it all wrong (or that the website did, or both). Hence, I would be grateful for corrections. My apologies for not being able to provide the link. The...
9. ### Is There an Easier Way to Calculate 3D Rotation Matrices?

While resolving a problem in mechanics I discovered a beautiful and easy way for finding out what the rotation matrices in 3 dimensions are! And I'm surprised that I do not find this method anywhere on the internet! Would it be because it's not technically correct? Anyways, here it is: It's all...
10. ### Exploring the 3 Dimensions of Space and Time

Why do we see the dimensions of our universe as 3 dimensions of space and time instead of space, time, and matter? (Or another variation)
11. ### I Double slit experiment in 3 dimensions?

Has anyone performed the double slit experiment in three dimensions? By this I mean, having double slits and a detection screen on three sides? This would imply there are 6 slits and 3 detection screens. What would we observe? Would we see the electron exhibiting wave like behavior (ie...
12. ### B Visualizing Spacetime: 3 Dimensions Not Enough?

I've tried to imagine and draw the effect of a large object would have on space time in 3d but it just doesn't seem right. Would I be right to assume that maybe spacetime has more than 3 dimensions?
13. ### General Motion of a particle in 3 dimensions

Homework Statement Particles of mud are thrown from the rim of a rolling wheel. If the forward speed of the wheel is v0, and the radius of the wheel is b, show that the greatest height above the ground that the mud can go is b + v02 / 2g + gb2/ 2v02 At what point on the rolling wheel does this...
14. ### Spring Compression (x-x0) = .00579 m

Homework Statement A spring (k = 2900 N/m ) is compressed between two blocks: block 1 of inertia 1.70 kg and block 2 of inertia 2.00 kg. The combination is held together by a string (not shown in (Figure 1) ). The combination slides without spinning across low-friction ice at 2.90 m/s when...
15. ### Bravais lattices in 2 dimensions (and 3 dimensions)

I'm reading M. Omar Ali's Elementary Solid State Physics and in it, in Subsection 1.4 The Fourteen Bravais Lattices and the Seven Crystal Systems he says that "..., but one cannot place many such pentagons side by side so that they fit tightly and cover the whole area. In fact, it can be...
16. ### Newton's Method generalized to 3 dimensions

Homework Statement Prelim: my question is about a very specific part of a question whereby the student is asked to derive the final formula for the general solution in two vars, but I will post the entire question for clarify. Newton's Method for approximating the roots of an equation f(x)=0...
17. ### Fitting an ellipse through 3-d data

Hey, sorry if this is not the right section to post in, the topic is a bit ambiguous. I've generated a set of coordinate points for the orbit of Mercury (3d cartesian) and now I want to fit an ellipse through it so I can get an accurate estimate of the location of the perihelion. I am using...
18. ### Confused about force and work in 3 Dimensions. Line integrals.

So I am kind of confused about the role of force when calculating work. Specifically, when defining work using a line integral. There is a paragraph in my calculus book that is really throwing me off and its really bugging me so much I can't continue reading unless I fully understand what's...
19. ### Elliptic geometry in 3 dimensions

I'm interested in elliptic space from an intrinsic point of view(manifold pov) rather than the models based in Euclidean embeddings. Would it be correct to say that the isometry group of this geometry is isomorphic to SU(2), i.e.:versors or unit quaternions?
20. ### Does energy level determine degeneracy in 3D systems?

Hi everyone. I can not remember if, in 3D, the higher it is the energy level, the higher it is its degeneracy. With a cubic well and with a 3D harmonic oscillator it holds... Does anyone know if it is a general rule or not (and in the case it is, where does this rule come from)?
21. ### Impossibility of having less than 3 dimensions?

I have heard of Flatland and seen many analogies regarding a 2 dimensional world but, can such exist? Considering that even subatomic particles move in 3 dimensions then am I to assume that a 2 dimensional world is an impossibility? Even a line is 3 dimensional for if a line were only 1...
22. ### Vector equation for a line segment in 3 dimensions

Homework Statement Find the vector equation for a line segment from (2,-1,4) to (4,6,1). Homework Equations Arithmetic :p The Attempt at a Solution What I did was that I simply solved for the distance between the two points and used it as my vector, I then said <4-2t, 6-7t...
23. ### 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...
24. ### 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 +...
25. ### Finding the work done using force vectors in 3 dimensions

Homework Statement Find the work done by a force acting in the direction 2i - 5j + k in moving a particle from (3, 3, 1) to (1, 2, 4). Homework Equations The Attempt at a Solution I just found the displacement vector (2,1,-3) and did the dot product with the force vector...
26. ### Simple problem with vectors in 3 dimensions

Homework Statement Three cables are used to tie the balloon shown in the figure. Determine the vertical component of the force P exerted over the balloon at point A, if the tension on cable AB is 259 N. http://img521.imageshack.us/img521/9687/physicsballoonproblem.png (Sorry for the figure...
27. ### Special relativity relating 3 dimensions

Homework Statement An event happens in frame S at x=100m y= 10m z=1m at time t=2*10^-3s. What are the coordinates of this event in rame S' that is moving with velocity v=0.92c (ihat) and the orgins coincide at time t=0. Homework Equations Lorentz transformations The Attempt at a...
28. ### Vector Question: 3 dimensions inside a rectangular soild?

Vector Question: 3 dimensions inside a rectangular soild?? Homework Statement Three forces of 5 N, 8 N, and 10 N act from the corner of a rectangular solid along its three edges. a. Calculate the magnitude of the equilibrant of these three forces. b. Determine the angle that the equilibrant...
29. ### Length of a line in 3 dimensions

All, I am trying to determine the length of line across 3 dimensions (XYZ). My X&Y are WGS 84 coordinates and my Z value is HAE (Height Above Ellipsoid) in meters. I can determine the XY length on a plane, but how do I account for the additional length added by a change in Height...
30. ### What is the tension in the rope attached at -4mxˆ?

Homework Statement A 100kg mass is supended by 3 ropes. one rope is attached at a point 1mxˆ + 1myˆ, one is attached at 1mxˆ - 1myˆ and one is attached at -4mxˆ. The three ropes all connect at -1mzˆ, at which point the mass is attached. What is the tension T in the rope attached at -4mxˆ...
31. ### Vanishing Ricci Tensor in 3 Dimensions

In my general relativity course my professor recommended that it would be useful to convince ourselves that in 3 dimensions the vacuum field equations are trivial because the vanishing of the Ricci tensor implies the vanishing of the full Riemann tensor. However, I am unsure of how to show this...
32. ### Statisics - linearity and best-fit in 3 dimensions

Howdy folks I've gotten a number of answers to this in various fora, some contradictory. I need to do 3 things to a set of datapoints in 3space (X,y, and z real values). 1)Test for linearity (pearson's R?). 2)If passed, find line of best fit (SSE?) 3)See if line of best fir is...
33. ### Finding the equation of a straight line in 3 dimensions.

Homework Statement Prove that the shortest path between two points in three dimensions is a straight line. Write the path in the parametric form: x=x(u) y=y(u) z=z(u) and then use the 3 Euler-Lagrange equations corresponding to ∂f/∂x=(d/du)∂f/∂y'. Homework Equations Stated them...
34. ### Mathematica Mathematica: NDSolve in 3 dimensions

Hi I am trying to solve Newtons equation for a particle in (x, y, z) using NDsolve. Here I what I have so far: sol = NDSolve[{ x''[t] == acceleration[x'[t], y[t], z[t]], y''[t] == acceleration[y'[t], x[t], z[t]], z''[t] == 0, x[0] == 2, x'[0] == 0, y[0] == 0, y'[0] ==...
35. ### Rotation in 3 dimensions about a point

Hi, I was wondering whether it's possible to define a rotation in 3 dimensions about the origin. Is it necessary to define an axis of rotation or would it be legal to say that you rotate abput the origin (like a phasor in 3 dimensions.) Thanks!
36. ### Equation of a curve in 3 dimensions

Homework Statement A heat-seeking missile is located at (2,-3) on a plane. The temperature function is given by T(x; y) = 20-4x^2-y^2. Find the equation of the curve along which the missile travels, if it continuously moves in the direction of maximum temperature increase. Express your...
37. ### Vectors of 3 components (3 dimensions)

Hi, I don't think my textbook gives much information on vectors in 3 dimensions. The first chapter is on vectors, but only uses 2 and 1/2 pages to explain vectors in 3 dimensions. I have found a wealth of information on vectors in 2 dimensions (there are literally hundreds of detailed videos...
38. ### Properties of curvature tensor in 3 dimensions?

Is there any properties with the curvature tensors in 3 dimensions? (Maybe between the Ricci tensor and the Ricci scalar, they are proportional to each other? ) I heard about it in a lecture, but I can not remember the details. The 3 dimensional case is not discussed in many reference books...
39. ### Finding the work done using force vectors in 3 dimensions

Homework Statement Find the work done by a force of 3 Newtons acting in the direction 2i + j + 2k in moving an object 2 meters from (0, 0, 0) to (0, 2, 0). Homework Equations Commonly known vector operations. The Attempt at a Solution I found the displacement vector to be 2j...
40. ### How do I find the magnitude of the sum of these force vectors in 3 dimensions?

Homework Statement [PLAIN]http://img406.imageshack.us/img406/3756/fmp1.jpg How do I calculate the magnitude of the sum of these 3 vectors? Also, how do I find the angles the sum of the vectors make with each axis? F1 = 260N F2 = 75N F3 = 60N Homework Equations F = F1 + F2 + F3The Attempt at a...
41. ### What made the universe have 3 dimensions, instead of some other number?

I think because the number 3 is still pretty low it isn't so suspicious to people, but imagine we lived in some universe with, say, 186 dimensions (that miraculously supported intelligent life, so there's someone to ask the question - I know about the anthropic principle). Wouldn't we have asked...
42. ### How would a 2 dimensional intelligence find out the world has 3 dimensions

could you apply this to humans who are 3 dimensions and discover a 4 dimensions?
43. ### Calculating Drag in 3D with Different Areas & Coefficients

Okay, thanks Hikaru and K2 for your help on the accelerated drag problem. Now I have another drag related problem I wonder if you you help me with. Say a car is put in a wind tunnel and is measured to have the following attributes: Frontal Area: Ax Side Area (Right): Ay Frontal Coefficient of...
44. ### What's special about 3 dimensions?

I wonder why it took me so long to ask this question. But it's better late than never. Space has 3 dimensions. I have read numerous books where there are creatures who live in 1-D space, there're also hypothetical creatures who live in a 2-D space. But I don't remember reading a book where...
45. ### Method for rotating data points in 3 dimensions

My best guess is this fits in algebra, I've been scratching my head with this for a while. I have a three dimensional array representing points of certain objects in a game. int [5,5,5] currentLocs I want to be able to rotate these 3d points around the center in any direction by 90...
46. ### 3 dimensions of space and 1 of time

I'm wondering if the perception of spacetime as "3 dimensions of space and 1 of time" is a symptom of our inability to maintain an objective view on the matter. I believe the reason we separate them in our minds is because we seem to have some control over space but no control over time. But...
47. ### Finding coordinates in 3 dimensions.

Homework Statement Consider a Cartesian coordinate system, with units measured in 1000 feet, and with the z = 0 coordinate plane lying on the ocean surface. Two ships A and B, moving at speed 250 feet/min, are located at (4,0,0) and (0,5,0), moving North (-x direction) and West (-y direction)...
48. ### Distance formula in 3 dimensions

Edit*: problem solved. Thanks for the hint Dick.
49. ### 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?
50. ### 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...