Dimensions Definition and 1000 Threads

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...

Is it possible for an object with 6 dimensions to exist in a three dimensional universe?

Advanced Calculus of Several Variables, 5.6: Two vector spaces V and W are called isomorphic if and only if there exist linear mappings S : V \to W and T : W \to V such that S \circ T and T \circ S are the identity mappings of S and W respectively. Prove that two finite-dimensional vector...

Galileo shows that, if any effects due to air resistance are ignored, the ranges for projectiles on a level field whose angles of projection exceed or fall short of 45 degrees by the same amount are equal. Prove this result. A: So ,I tried these vx = v*cos(q) //q is the shooting angle, vx is...

I have reading about cosmic strings and have some questions about them, are they in any way related to other dimensions even though they are one dimensional? Also do they have anything to do with gravitons and the cause of gravity?

Homework Statement A particle leaves the origin with a velocity of 7.2 m/s in the positive y direction and moves in the xy plane with a constant acceleration of (3.0i - 2.0j) m/s2. At the instant the particle moves back across the x-axis (y=0), what is the value of its x coordinate...

Hi, I'd be grateful if someone could tell me whether these proofs I've done are correct or not. Thanks in advanced. Let V be an n-dimensional vector space over \mathbb{R} Prove that V contains a subspace of dimension r for each r such that 0 \leq r \leq n Since V is n-dimensional...

How hard is that SF? – Pharyngula mentions a survey that someone once did, asking people to rate various science-fiction movies on two dimensions. Hard: a work "takes great care in accurately presenting then-known scientific facts". Soft: a work "often and casually violates our understanding...

I have a few questions so I hope it is okay if I ask them all here in this thread. They are all related somewhat. According to brane cosmology, our 4-D universe is embedded inside a higher dimensional space, a hyperspace if you will, called the bulk. The reason we cannot perceive or interact...

So say I have a n-1 form \sum^{n}_{i=1}x^{2}_{i}dx_{1}...\widehat{dx_{i}}...dx_{n} and I want to find the exterior derivative, how do I know where to put which partial derivative for each term, would it simply be?? \sum^{n}_{i=1}...

On all manifolds dimension 1-3, there is only one differential structure per manifold, yet in higher dimensions it seems to follow no pattern. Is there a physical reason why you can construct a certain number on any given dimension? Also, what is it about dimension 4 that is so strange? Using...

Problem: A hockey puck rebounds from a board as shown in figure 16. The puck is in contact with the board for 2.5 ms. Determine the average acceleration of the puck over the interval. t = 0.0025 s |vi|= 26 m/s |vf| = 21 m/s aav = ? *v and a are vectors* I have made several attempts to...

Hi all, I was deriving the free electron gas for practice in 1, 2, and 3 dimensions, and I started wondering why they have different dependencies on energies and what that means. I got: 1D: ##g(E) = \frac{1}{\pi\hbar} \sqrt{\frac{2m}{E}}## 2D: ##g(E) = \frac{m}{\pi\hbar^2}## 3D: ##g(E) =...

find the dimensions of the largest rectangular box with a square base and no top that can be made from out of $1225 in^2$ of material. well, this might be over simplified but since the volume is max of cube to the a surface area I thot making a cube out of the material would be max volume...

Hi! :) I'm trying to calculate the appropriate lenses to use for a project. I need to magnify a 50mm by 50mm square image that is 40mm from a magnifying lens (with a radius of 12.5mm). Due to size constraints, I also have a thin prism to redirect the light. Assume the viewer (an eye) is...

Hi all. I'm trying to solve this PDE but I really can't figure how. The equation is f(x,y) + \partial_x f(x,y) - 4 \partial_x f(x,y) \partial_y f(x,y) = 0 As a first approximation I think it would be possible to consider \partial_y f a function of only y and \partial_x f a function of only...

How do you calculate an object in 4 dimensions? Like the 4 dimensional cube. I understand that a point is the beginning of a line and a line is the beginning of a plane. From there a plane translates into a 3 dimensional object. A 3 dimensional object translates into a 4 dimensional thing... I...

Homework Statement the perimeter of a rectangle is 24 ft. the length is 4 ft longer than the width find the dimensions width x length x+4 however, I should be doing it like this: a first equation should start like: 2x+2y=? and the second should start like x=y+? so what's the...

If we assumed an empty space, but also assumed space dimensions are closed ( repeat after some distance D ), what would the metric tensor look like? Is this just equivalent to a space with a constant curvature R? If so, how does R relate to D? Would the time dimension also necessarily be...

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...

Hello all, I am currently doing a design project on gyroscopes. My question concerns the flywheel design, specifically trying to determine the dimensions of a flanged free-spinning flywheel to maximize the moment of inertia while trying to minimize the mass, given certain design constraints...

Hairy ball theorem - Wikipedia is not as good or as well-referenced as I'd hoped, and it mainly discusses vector fields on the 2-sphere, the ordinary sort of sphere. In particular, it does not mention the minimum number of zero points of a continuous vector field on a sphere. I would guess...

Homework Statement Let f : ℝ2 -> ℝ be some function that is defined on a neighborhood of a point c in ℝ2. If D1f (the derivative of f in the direction of e1) exists and is continuous on a neighborhood of c, and D2f exists at c, prove that f is differentiable at c. Homework Equations...

Given that string theory is built on the idea of one-dimensional entities, which seems much too "nice" given the general fuzziness of interpreting quantum mechanics, would it be possible for a universal theory to be based on a non-integer number of dimensions? I basically know nothing of...

I am a little confused about dimensions, if the nullspace of a matrix is spanned by the 0 vector, does that mean the dimension of the nullspace of this matrix is 0? In the problems I attached, both A and B reduced to the identity matrix. Note (2) is supposed to be dim(N(B)) and dim(col(B))...

A worker works in a roof and let's a hammer fall over the roof with the speed 4m/s.The roof forms an angle 30 degree related to the horizon and its lowest point its 10meters from the ground.What is the horizontal displacement of the hammer from the moment he leaves the roof to the moment he...

I'm wondering what the Dirac delta of a function would be in n dimensions. What is {\delta ^n}(f(x))? I understand that in 3 dimensional flat space, the Dirac delta function is {\delta ^3}(x,y,z) = \delta (x)\delta (y)\delta (z) and {\delta ^3}({{\vec x}_1} - {{\vec x}_0}) = \delta ({x_1}...

Every picture I've seen to illustrate wormholes is always a shortcut from one point on a 2D surface to another. And it's easy to see that the distance is shorter through the wormhole since we are view it from a 3D perspective. This makes me wonder if higher dimensions are required to construct...

1. On a table (defining the x,y-plane laying 3 identical coins A,B and C with identical diameter of 18.00mm. The coordinates of their centers are Z(0,0), Y(60.0,0), X(60.0, 45.0) all given in mm. Under what angle relative to the x-axis one has to push Z against Y so that Z performs after the...

Greetings, This is basically just an observation I expect it to be laughed at (already has been laughed at in the mensa forum) but you know what they say - the only stupid questions are the ones left unasked and what better way to put it to rest than to ask some real hard core physicists... I...

hello.i need to add chlorine to an OVERHEAD water tank.for that i need to know the proper quantity of chlorine to be added.and for that i need to know the tank capacity.unfortunately i do not know the dimensions of the tank,neither i have drawing of it..BUT...a vertical inline pump sucks water...

I've attached the problem. For S: I form the matrix: 1 0 0 1 0 0 0 0 Thus the dimension is 2. For T: I form the matrix 0 0 1 0 0 1 0 0 Thus the dimension is also 2. Is that the correct idea? Also what does S ∩ T mean? I couldn't find the symbol in my textbook.

Homework Statement Fast Eddie McSpeedy is a receiver for the Kennesaw Kilowatts in the Metro Metric Football League and Big Bobby Clobber plays defense in the rival Marietta Megatons. Eddie has a mass of 85 kg and Bobby has a mass of 140 kg. Eddie catches the ball and runs eastward at 2.4 m/s...

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...

Suppose we have a mxn matrix, where each row is an observation and each column is a variable. The (i,j)-element of its covariance matrix is \mathrm{E}\begin{bmatrix}(\vec{X_i} - \vec{\mu_i})^t*(\vec{X_j} - \vec{\mu_j})\end{bmatrix}, where \vec{X_i} is the column vector corresponding to a...

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...

Homework Statement A car initially traveling due north goes around a semicircle having a radius of 500 m at a constant speed of 20 m/s. A) How long does this take? B) What is the magnitiude and direction of the average acceleration? Homework Equations a = Δvx/Δt(xhat)+Δvy/Δt(yhat)...

In this excerpt from the notes of Sean M. Carrol, he says: "Einstein’s equations may be thought of as second-order differential equations for the metric tensor field gμν. There are ten independent equations (since both sides are symmetric two-index tensors), which seems to be exactly right...

I can easily visualize the 3 dimensional way to do so, and already have. I'd like to rotate from the (-1,-1,-1,-1) -- (1,1,1,1) line to the x-axis (-1,0,0,0) -- (1,0,0,0). To do so in 3 dimensions (-1,-1,-1) -- (1,1,1) line to the x-axis (-1,0,0) -- (1,0,0) I rotated around the z...

Homework Statement A tennis player standing 8.0 meters from the net hits a ball 1.5 meters above the ground toward her opponent. The ball leaves her racquet with a speed of 25.0m/s at an angle of 14.0 degrees above the horizontal. The net is 1.0 meters high. The baseline is 12 meters back...

According to M-theory as I understand, the 7 additional spatial dimensions to our familiar 3 are curled up all around us but they are too small for us to see. However I have difficulty in understanding how this constitutes a "dimension" because dimensions allow additional degrees of freedom...

Homework Statement A common dimensionless group used in heat transfer calculations is defined as: Nu=\frac{hD}{k} where h is the heat transfer coefficient, and D is the diameter of the pipe in which heat transfer takes place. Please determine the dimensions of the quantity k in...

Would someone here be able to write down for me an example of a metric on a manifold with both macroscopic dimensions, and microscopic "curled up" dimensions with some radius R ? Number of dimensions and coordinates used don't matter. Not going anywhere with this, I am just curious as to how...

Homework Statement Let P represent a force and x, y, and z represent distances. Determine the dimensions for each of the quantities listed below. I attached the problem I need help with. (it's a small picture) So I'm a bit confused since the it involves both dx and dy. The dimensions for P...

Homework Statement In the equation z = ct + d, z is measured in meters and t is measured in seconds. What are the dimensions (units) of d? answer options are... s/m, m/s, m, s, m*sHomework Equations The Attempt at a Solution plugged in m for z, s for t, and m/s for c. solved for D and got 0.

Homework Statement "A particle moves in the horizontal plane that contains the perpendicular unit vectors i and j. Initially it is at the origin and has velocity 18ims^-1. After accelerating for 10 seconds its velocity is (30i + 8j)ms^-1. Assume that the acceleration of the particle is...

hello all I am so glad to have found this forum. I've always had an interest in astrophysics, cosmology, SR/GR, etc, and no place to ask questions. I'm an engineer and was once a member of Mensa (I only left the organization because I thought other members were crazy. Sorry). So although I'm...

Weinberg wrote that in 3D and higher spaces all particles must be bosons or fermions. The proof used the fact that particles are really indistinguishable i.e. we can't "mark" any particle and the mathematical replacement of two particles of the same type should not change any physical...

If we have a unit circle within a square s.t. the square touches the circle in 4 places then the biggest gap we can find is just √2 - 1. Doing a similar thing with a sphere in a cube we get √3 - 1 I've heard the n-dimensional analogue is √n - 1. Which is crazy as it means the gap is bigger...

Here's what i know about Dimensions... Infinite stacks of a 1D world makes a 2D world, And Infinite stacks of a 2D world makes a 3D world and Infinite stacks of 3D world makes a 4D world and so on... So if we humans are 3D creatures, then we perceive 4th D as time, Same goes for 4D creatures...