Dimensions Definition and 1000 Threads

Hello, Let's start with a cellular decomposition of 3-space, a "foam". A foam can be represented by its dual graph: cells and faces are dual to vertices and links. What about the opposite? It is clear that one can construct graphs for which no dual foam exists: take a large foam and...

1. Is it possible to calculate the capacitance of a system where the top plate has the dimension d1 and the bottom plate has a dimension d2 and d1<<d2. Now, the difference between the plates are t. Is it possible to calculate the capacitance of this system where the dielectric is oil? 2. In...

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...

Is a curve (Say 'S') 1d or 2d? I ask this question because for so long i was under the impression that it was 2d, since we need a 2d cartesian plane to draw and describe a curve. But then i read in a popular book that it was 1D, which is hard to believe. so which is it?

Why do we call them 3 dimensions when all that they are, are just the ability of movement in space? Physical movement cannot be restrained in any vector. It takes place in a 3 dimensional dimension. Thus 1 dimension is physical movement in space and the second dimension is time. Within the 1st...

Homework Statement Let v = 1 / kt v = m/s k = 1/m t = s v = dx/dt so dx = dt / kt integrating, x = ln (kt)/k + C However the argument of a logarithm is dimensionless. But an integration is a perfectly normal thing to do. So how come this integration results in a...

Homework Statement How do you find the volume of three dimensions. 2.52x4.57x5.61 Homework Equations The Attempt at a Solution All you have to do is multiply the three right So the answer would be 64.607004? Thanks

I've been reading all about dimensions and started theorising myself , can there be something like -1D? The theory I came up is this: The Minus Dimensions don't have an object (it doesn't exist), but it's form is created by the location, which is other specific positive D objects. For...

How do you derive the hypervolume/hypersurface of the unit ball in n dimensions? I thought it'd be trivial but oh well. I'm guessing switch to n-D spherical coordinates? Is there an argument which doesn't involve explicitly calculating too many things? :x

I have a rectangular sheet of given dimensions say L wide and H high. Out of each point some variable field is flowing through given by rules as follows: Consider the top left corner of the sheet, the field is perpendicular at that point. As one moves from top left corner to the top right...

According to string theory, are strings Planck length in 1 dimension and 0 in all other dimensions? Or more than Planck length in 1 dimension and exactly Planck length in all other dimensions? Or something else? Thanks.

Homework Statement I need to find the values of thickness (t), mean diameter (D) and mean length (L) that will give the minimum area for the streamlined section, given that it's moment of inertia is 5.42 in^4. Homework Equations (the I's and A's after all K's here are meant to be subscripts...

Hi, I was thinking about Knot Theory for a while and started thinking about higher dimensionalities. Could the knots we know so well (knots in 3d space) be undone if allowed to be manipulated through a fourth spatial dimension? Could they be made topologically equivalent to the unknot? And if...

Greetings. My question comes in two parts. Part one - In most "low-level - made for t.v." explanations of the extra dimensional space they describe these extra dimensions as "curled-up". If I were to visualize the extra dimensions of string theory would it be better to think of these extra...

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...

Homework Statement three distiguishable spin 1/2 particles interact via H = \lamda ( S_1 \cdot S_2 + S_2 \cdot S_3 + S_3 \cdot S_1 ) a) What is the demension of the hilbert space? b) Express H in terms of J^2 where J = S_1 + S_2 + S_3 c) I then need to find the energy and...

Homework Statement Three students push a box. Michael pushes with a force of 200 N at 0 degree. Shannon exerts a force of 150 N at 30 degrees, and Adam pushes with 175 N at 145 degrees. What is the magnitude of the net force? Homework Equations Some trig nothing special The Attempt...

Do you know of any papers about spin in dimensions>4? It seems that there are two independent spins in 4+1 dimensions, since you can replace spatial dimension 1 with 2 and 3 with 4, each pair not messing with the other. I found only one paper on arxiv: <http://arxiv.org/abs/0908.2484> on 5D...

Homework Statement One object is traveling in the x direction at 0.935c and another is traveling at 0.98c in the z direction. Determine the overall velocity of the second object from the point of view of the first object. Homework Equations v'x=(vx-v)/(1-vx*(v/c^2)) The Attempt at a...

the top and bottom margins of a poster are 2cm and the side margins are each 4cm. If the area of printed material on the poster is fixed at 382 square centimeters, find the dimensions of the poster with the smallest area. so the area l*w = 382 and the perimiter = 2(l-4)+2(w-8) but if i...

A radioactive nucleus of mass 5 × 10–26 kg is at rest and emits two neutrons, each of mass 1.6 × 10–27 kg, at right angles to each other. If both have speeds of 360 m s–1, calculate the recoil speed of the nucleus. I named calculated the neutrons and named them p1 and p2. Since p1 = p2...

Homework Statement Given: electromagnetic tensor F(superscript)uv: electromagnetic tensor F' after the lorentz transformation: [ 0 -Ex -gamma(Ey-VBz/c) -gamma(Ez-VBy/c) Ex 0...

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...

Homework Statement Find the dimensions of the following linear spaces. a. the real linear space C^3 Homework Equations n/a The Attempt at a Solution So I'm not really sure what C means. I know it's the smooth functions and I think raised to the 3rd power means it the functions...

Hello :smile: I was hoping someone could help me with this mechanics problem. Homework Statement A particle of 2kg mass moves in three dimensions under the action of a force \underline{F}=6\underline{i}-6t^2 \underline{j}+(4-2t)\underline{k}. At t=0, it is at rest with position...

Homework Statement Homework Equations Moment of Inertia equation: I=(1/12)bh^3 Stress and Strain equations: Sigma= -(M*c)/I Tao = (V*Q)/(I*t) The Attempt at a Solution I know I need to use shear and moment diagrams to find the max moment so I can use the Stress diagram to...

Homework Statement a ball of mass 2kg is traveling North with a Velocity 6m/s when it collides with an identical, stationary ball. after the collision, one of the ball moves with a velocity of 2m/s at an angle of 30deg east of north. find Velocity of the other ball. m1=2kg m2=m1 v1=6m/s...

Hello; I am curious about how many dimensions there are in physics. My physics teacher responded with '10 or 11'. -1 dimension: ? 0th dimension: Fixed point 1st dimension: Line 2nd dimension: Flat plane 3rd dimension: Object with depth on a flat plane. 4th dimension: 3-dimensional...

Hi, I have no knowledge of ST but have a probably simple question. I saw a program about how the extra dimensions of space in string theory are curled in on them selves. What I want to know is if they really are the same dimensions. Say for example if there are 11 dimensions and I would pick...

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...

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)...

Hi =D I was thinking about the physical units (g, m, s, K, J, A, V, etc). I know we got a thing in physics called dimensional analysis, so you analyse some variable that you know it depends on other variables and the two sides of the "equation" (I mean a equation with the proportional sign...

Hi everyone , this is my first time here :) My question is simple , if gravitation is basically a space distortion so it's fair to say that at least a fourth dimension exists , since a distortion must occur in higher dimension than the one of the concerned space . Is it correct putting it...

Hello all, I'm trying to design an efficient airfoil for a wind turbine blade. To be entirely honest, I'm not entirely familiar with this field of engineering; I mainly specialize with steam applications, so this design attempt is obviously a somewhat far cry from that! Yet I've been trying...

helloo! i'm trying to find the Green's function for the modified heat equation $u_t = t * grad(u) $ in n dimensions using scaling arguments. I know how to do this for the regular heat equation, by switching to polar coordinates and noticing that the equation and initial conditions are...

There is the possibility that spacetime has more than 4 dimensions, and that the additional dimensions are curled up not at the Planck scale but at some larger scale. There has been some discussion that if these extra dimensions exist, then the LHC might produce microscopic black holes (which...

hi everyone, i am no physicist so i only have a slight understanding of these matters. I just finished reading Greene's "elegant universe" and i understood that in "classical" string theories there are 6 compactified dimensions along with our familiar 3 extended spatial dimensions + time...

Homework Statement I've completed the derivation of the hypersphere volume for integer dimensions, and my solution matches what's on Wikipedia. How can I generalize it to fractional dimensions? Homework Equations The Attempt at a Solution Not a clue; my only guess at this point...

Im working through derivations of string equations of motion from the Nambu-Goto Action and I'm stuck on something that I think must be trivial, just a math step that I can't really see how to work through. At this point I've derived the equation of motion for the closed string from the wave...

Hey I have this plate, and as you can see it has 4 bolt connections and no other. When applying the load bending will occur in the plate. I am interested in making the diameter of bolt as small as possible. My problem is though that I only can see the shear forces in the plate. How can I...

Homework Statement Hi! This is from Physics for Scientists and Engineers, Vol. 6 by Tipler and Mosca. 44. Kepler's third law relates the period of a planet to its orbital radius r, the constant G in Newton's law of gravitation, and the mass of the Sun Ms . What combination of these factors...

String theory requires 9 spatial dimensions, M-theory 10. One followup to Verlinde's paper is this: http://arxiv.org/abs/1002.0488 Hidden symmetries for thermodynamics and emergence of relativity Liu Zhao (Submitted on 2 Feb 2010) Verlinde recently proposed an idea about the thermodynamic...

Homework Statement In the game of darts, the player stands with feet behind a line 2.36 m from a dartboard, with the bull's-eye at eye level. Suppose you lean across the line, release a dart at eye level 2.23 m from the board, and hit the bull's-eye. Find the initial velocity of the dart, if...

Edit*: problem solved. Thanks for the hint Dick.

it seems that the vector product between vectors in three dimensions is peculiar property of the three dimensional space

Homework Statement Two spacecraft from different nations have linked in space and are coasting with their engines off, heading directly toward Mars. The spacecraft s are thrust apart by large springs. Spacecraft 1, with a mass of 1.9 x 10^4 kg, then has a velocity of 3.5 x 10^3 km/h at 5.1...

If we start with minkowski spacetime in 4 dimensions and then add several curled up spatial dimensions attached at every spacetime point, then: I'll label a spacetime point as: (ct,x,y,z)[a1,a2,a3,..,an] where the bracketted coordinates are the 'curled' coordinates. - If we label the...

what problems are solved by the theory of 11 different dimensions instead of just 1-4 proposed in the m theory and string theory

How does one know that chemical, atomic, and nuclear reactions occur in three spatial dimensions? Why not four, or two, or negative pi, or sixty-seven dimensions? And yes, I know the last two are implausible.

Special Relativity vs. "Curled up" spatial dimensions To be more specific I mean the 3 familiar spatial dimensions not extra ones(unless I guess they are large enough for SR to be effective). Anyway, I was reading a book on Superstring Theory(Which is why I say not extra ones it proposed extra...