Dimension Definition and 881 Threads

Homework Statement A car accelerates at 2.10 m/s2 along a straight road. It passes two marks that are 29.6 m apart at times t=4.10 s and t=4.90 s. What was the car's velocity at t=0? I'm assuming the car has constant acceleration of 2.10 m/s2 Given \Deltax = 29.6 m a = 2.10 m/s2 vi = ...

Homework Statement A hot air balloon is ascending straight up at a constant speed of 8.10 m/s. When the balloon is 13.0 m above the ground, a gun fires a pellet straight up from ground level with an initial speed of 28.0 m/s. Along the paths of the balloon and the pellet, there are two...

i am now studying dirac equation and klein paradox if we confine to one dimension, we only need one alpha matrix, not three so in lower dimensions, maybe the dirac spinor is not of four components but fewer? i am curious about this question because it seems that as for the Klein...

So do we know for sure what the 4th spatial dimension is? I have read in many places that it is time. I would say this makes sense because we are perceiving time in 3 dimensional slices in our dimension. The same way a 2D being would perceive 2D slivers of a 3D object in its own dimension.

I see lots of references to time being the fourth dimension as well as there being 3 + 1 dimensions to spacetime as we know it, etc. I also see that time has to be treated differently in some of the constructs of physics. So it seems that time seems to be both similar and dissimilar to the other...

Suppose I have a basis for a subspace V in \mathbb{R}^{4}: \mathbf{v_{1}}=[1, 3, 5, 7]^{T} \mathbf{v_{2}}=[2, 4, 6, 8]^{T} \mathbf{v_{3}}=[3, 3, 4, 4]^{T} V has dimension 3, but is in \mathbb{R}^{4}. How would one switch basis for this subspace, when you can't use an invertible...

In Minkowski 4-D spacetime the cooridnates of an point are (ct,x,y,z). My question is why we multiply time with speed of light c and not some other speed v (speed of object moving in three spatial dimantions)? If we treat the time as a fourth dimension it would be more reasonable to say that...

Dear all, Is there a method to find the maximum and minimum dimension of an irregular closed loop? This is a problem when we want to define the full-width - half maximum of a image. The level contour of this image at its half maximum can be an irregular closed loop. Any reference or...

(Maybe this should go under General Math or maybe even Topology but since it's about the dimension of the universe I'll put it here. Feel free to move it.) I've had too much coffee and on one my frequent wiki binges - reading about life, the universe and everything - I've come up with a...

The possibility of "Perception" being a dimension? Is it possible that perception itself could be a dimension? Now think deeper, not personal perception, but instead the idea of perception in general. Because quiet simply, there are lots of things that exist that we cannot perceive. Just as...

Find the basis and dimension of the following homogeneous system: A = |1 0 2| |x1| |2 1 3| |x2| = [0,0,0] |3 1 2| |x3| My attempt: Solving the coefficient matrix for RREF, I get the identify matrix. So, x1=x2=x3=0 and the only solution is a trivial one. Does that mean...

Hello forum, today in my gr. 12 physics class I had a interesting question which I could not prove at all for the life of me. It is a really simple question, just with a little twist I suppose. As I was driving home from class I was thinking about what I was missing and thought up a solution...

Homework Statement He made some notes, but I'm still confused. The Attempt at a Solution

Hello, I just need to know whether or not surfaces with zero size in the third dimension, 6x8x0, is considered two-dimensional. The surface is there all the time. It has a location in the third dimension, so wouldn't it be a 3D object? I am not sure whether I should call a flat surface (as...

I've recently been learning about relativity and quantum physics. I understand it quite well now but i have a thought experiment that doesn't make sense. If i travel into the future through a high speed train and see the world blown up by some epic disaster, doesn't this mean that this was...

I have the following problem: I'm studying a system of polynomial equations in R^n and I'm looking at the surface which is the solution set of this system. I'm mainly interested in the dimension of this surface at a given point. Now, naively, one would try to compute the Jacobian (of the m...

So, I was just thinking what if the time dimension was a tiny curled up dimension like one of these supposed extra 8 dimensions from string theory ? If it allowed just enough wiggle room for objects to move the idea has some features that appeal to me. - time is symmetrical ; no past , no...

Hi forum, I was having some difficulty in understanding how time as a fourth dimension allows a cube of three spatial dimensions to obtain the properties of a tesseract. Suppose we allow a cube to exist for some interval of time. At the start such a cube would have eight vertices as well as...

I don't really understand what the dimension of a vector space for planes is. Is it 2 or 3 and why? What's the difference between the dimension of the plane as a surface (dimension of all surfaces is 2) and the dimension of plane in a vector space? Also, Wikipedia says that only planes passing...

Homework Statement A fugitive tries to hop a freight train traveling at a constant speed of 6.0 m/s. Just as an empty box car passes him, the fugitive starts from rest and accelerates at a=4.0 m/s2 to his maximum speed of 8.0 m/s. (a) How long does it take him to catch up to the empty box...

Homework Statement Calculate the following integrals: (a) I(n,\alpha) = \int_{0}^{\infty} e^{-\alpha x^2}x^n dx for n whole integers and n \ge 0 Calculate all results till n=5. Tip: First calculate I^2(0,\alpha) and I(1,\alpha) and then use this to calculate n>1. (b) I(n)=\int_{0}^{\infty}...

I suppose it might be appropriate here. I'm not really looking for an answer in pure maths (Topology is waaaaaaaaaaay beyond me), but rather in concept. Now, I can appreciate the properties of a tesseract, how it relates to and derives from the cube (I think of it as either putting 8 cubes...

I have a question in my linear algebra text that asks: Give integers p and q such that Nul A is a subspace of Rp and Col A is a subspace of Rq. What determines these values? Why are the values of p and q different between the Nul space and Col space? The matrix in question is a 3 x 4...

Is it the additional dimension, Time, added to the Euclidean (x,y,z) 3-D space? Or does it even make sense to ask this question? And instead consider 4D space-time (Minkowski Space) as a manifold in which 3D is embedded? I'm confused. :(

Issue with the definition of the Hausdorff dimension Homework Statement http://mathworld.wolfram.com/HausdorffDimension.html" involves a n-dimensional Hausdorff measure of 0. I'm having trouble understanding cases that would give such a value. Homework Equations the Hausdorff...

Homework Statement Find (a) a basis for and (b) the dimension of the solution space of the homogeneous system of equations. x - 2y + z = 0 y - z + w = 0 x - y + w = 0 Homework Equations The Attempt at a Solution (a) [1 -2 1 0] => [1 0 -1 2] [0 1 -1 1] => [0 1...

To remove an electron from a H-like atom, the action of a photon is required. But what is the dimension of a photon, that hits the electron? If it is considered a wave, then is it possible to have just energy without mass, and it is known that the extra energy of the photon is imparted to the...

Dear everybody... Could it be true... that Entanglement is made possible because the forces between the 2 electrons are being folded through a higher dimension, so there would be an explanation for the simultaneous reaction of the 2 electrons even if there`s a astronomical distance between...

Is string theory the replacement of the zeroth dimension? Or could it be thought of as such?

Homework Statement Tarzan is in the path of a pack of stampeding elephants when Jane swings into the rescue on a rope vine, hauling him off to safety. The length of the vine is 27 m, and Jane starts her swing with the rope horizontal. If Jane's mass is 56 kg, and Tarzan's mass is 91 kg, to...

Homework Statement Let S={v1=[1,0,0,0],v2=[4,0,0,0],v3=[0,1,0,0],v4=[2,-1,0,0],v5=[0,0,1,0]} Let W=spanS. Find a basis for W. What is dim(W)? Homework Equations The Attempt at a Solution i know that a basis is composed of linearly independent sets. This particular problem's...

what is 4th dimension? is it just 1 dimensional space? how come time is described as the 4th dimensional path? thanks..

In other words, why is dim[{0}]=0. My math professor explained that since the 0 vector is just a POINT in R2 that the zero subspace doesn't have a basis and therefore has dimension zero. This is not satisfactory. For example, I know R2 has a dimension 2, P_n has dimension n+1, M_(2,2) has...

I have a lab report due tonight. We were working on these in lab and I'm not sure how to tell which one was elastic or inelastic. We had three cases. We had to use the conservation of momentum and kinetic energy formulas.A ) Cart A and B have equal masses. Car B is at rest. Car A strikes car B...

I've been day dreaming about this idea for a month or two. There are many hypothesises that describe the universe in some higher number of dimensions. As far as I know, this is always an integer number of dimensions. I've been wondering if it is possible for the universe to have a...

New here. I just needed to tell my story somewhere. I'll warn you its not very interesting. Its just a strange thing that happened in my life and I cannot explain. I was detoxing of benzodiazepines at a medical detox center. I had a seizure. As a result I went into a coma or coma like...

So an example was the matrix: A = \left(\begin{array}{cccc} a&a+b\\ b&0\\ \end{array} \right) is a subspace of M2x2. and is the linear combination a*\left(\begin{array}{cccc} 1&1\\ 0&0 \end{array} \right) + b*\left(\begin{array}{cccc} 0&1\\ 1&0 \end{array} \right) Meaning it has...

If S is subspace of R6x6 consisting of all lower triangular matrices, what is the dimension of S? Does anyone know the properties about dimension of lower triangular matrices?

I need to ask a scientific community here if there are any sort of basis for the video and the book mentioned above in the title? once i got to the fifth dimension it all turned to non sense that does not relate in any way to string or M theory. Supposing I am right about what i said...

Is my understanding correct. Gravity is a week force because gravitons escape out of our dimension into other dimensions. If so would gravitons not also be able to re-enter our dimesion. Therefore cancelling out this theory

C[-pi, pi] Span(1, cos (2x), cos2 (x)) Doing the Wronskian here is pain so what other method would be more appropriate?

Homework Statement Prove true: For any subspaces U,V of R^n dim(U intersect V) <= min(dim(U), dim(V)) Homework Equations Min(a,b) = the minimum value of A and B The Attempt at a Solution I know this statement is true however I can't quite figure out where to start on how to...

Homework Statement Let U and V be vector spaces of dimensions of n and m over K and let Hom(subscriptK)(U,V) be the vector space over K of all linear maps from U to V. Find the dimension and describe a basis of Hom(subscriptK)(U,V). (You may find it helpful to use the correspondence with mxn...

Homework Statement My question is how to find the dimension of something. Let's say: x1-2x2+x3-x4=0 and let's do one with more than 1 equation. x1+x3-2x4=0 x2+2x3-3x4=0 Homework Equations The Attempt at a Solution For the second one I figured that if I took the...

e.g. For D=11, the M-theory, we require N=8, ... For D=10, we require N=16, or 32... ... So how to determine the number of supercharges, the \thetas, for arbitrary dimension, e.g. D=1, 2, ...

In am studying PDE and I have question about D'Alembert solution for one dimension wave equation. I am going to reference Wolfram: http://mathworld.wolfram.com/dAlembertsSolution.html [SIZE="6"]1) I want to verify the step of \frac{\partial y_0}{\partial t} of step (14) of the page...

Homework Statement V = the set of all symetrical nXn matrices, A=(ajk) such that ajk=akj for all j,k=1,...,n Determine the base and dimensions for V The Attempt at a Solution I set my matrix up as [a11 a12] [a21 a22] So a21 and a12 are equal to each other? I assume the...

Homework Statement V=R^{4}\ and\ a^{\rightarrow}, b^{\rightarrow}, c^{\rightarrow}, d^{\rightarrow}, e^{\rightarrow} \in V. (I'll drop the vector signs for easier typing...) a = (2,0,3,0), b = (2,1,0,0), c = (-2,0,3,0), d = (1,1,-2,-2), e = (3,1,-5,-2) Let\ U \subseteq V be\...

Homework Statement Find the dimnesion and a basis of vector space V Homework Equations V is the set of all vectors (a,b,c) in R^3 with a+2b-4c=0 The Attempt at a Solution (4c-2b,b,c) = b(-2,1,0) + c(4,0,1) so {(-2,1,0),(4,0,1)} is the basis of the SUBSPACE of V right? how do I...

Homework Statement A commuter travels between two stations. the stations are only 1.00km apart which means the train never reaches maximum crusing speed. The engineer minimizes the time interval (delta t) between the two stations by accelerating for a time interval (delta t sub 1) at a rate...