Dimension Definition and 908 Threads

I've been thinking about this problem of how we could possibly visualize the fifth dimension. The fourth dimension is easy enough as all you have to do is view a 3D projection of the object as it moves through 3D space. If you look at animations of the projection of a 4D hypercube you'll know...

Suppose that the position vector for a particle is given as a function of time by vector r (t) = x(t)i + y(t)j, with x(t) = at + b and y(t) = ct^2 + d, where a = 1.70 m/s, b = 1.05 m, c = 0.126 m/s2, and d = 1.12 m. So, I evaluated x(t) and y(t) at each time: x(t): 1.70*2.05+1.05 which...

Hello all, I have these two sets (I couldn't use the notation {} in latex, don't know how). V is the set of matrices spanned by these 3 matrices written below. W is a set of 2x3 matrices applying the rule a+e=c+f \[V=span(\begin{pmatrix} 1 &1 &1 \\ 1 &3 &7 \end{pmatrix},\begin{pmatrix} 0 &0...

Hey there peers :smile: I'm really keen on explaining science to others and I've been practicing it with my classmates lately, so I thought why not give it a try and make my first ever youtube video about a seemingly hard concept which is a space of 4 dimensions. I made this post just because...

While doing some ASME code calculations for a pressure vessel subject to external pressure I was wondering what'd be the optimum L/D ratio for a vessel that is subject to buckling under external pressure. For a given volume & Pressure. Could a general L/D ratio be derived or would it change...

Projectile motion consist of horizontal and vertical motion. The horizontal motion consists only of constant velocity, that is, the velocity of the object The vertical motion consists only of constant acceleration, that is, acceleration due to gravity. Yet... we have vx = vcos and vy =...

Our professor's notes say that "In general, in Hamiltonian dynamics a constant of motion will reduce the dimension of the phase space by two dimensions, not just one as it does in Lagrangian dynamics." To demonstrate this, he uses the central force Hamiltonian...

Want to understand a concept here about dimensions of a function. Using example 1: a simple Fourier series from http://en.wikipedia.org/wiki/Fourier_series s(x) = \frac{a_0}{2} + \sum ^{\infty}_{0}[a_n cos(nx) + b_n sin(nx)] So do we now say that s(x) has an infinite dimensional...

I'm a little confused by extra dimensions. People seem to say different things about the 'extra dimensions. Everyone seems to say that there are 3 basic dimensions (width, height, depth), however some people say different things about what additional dimensions are, just wondered if someone can...

We used to classify signals as 1D and 2D etc ie one dimensional and two dimensional. For example a periodic square wave signal is 1D and an image is a 2D signal etc (reference - Signals and systems by Simon Haykin and Barry Van Veen, 2nd edition , page 2). But the same periodic square wave...

Homework Statement A 100-kg uniform rectangular plate is supported in the position shown by hinges A and B and by cable DCE that passes over a frictionless hook at C. Assuming that the tension is the same in both parts of the cable, determine (a) the tension in the cable, (b) the reactions at...

Homework Statement This problem concerns a collision experiment performed on a frictionless surface with gliders A and B, with masses m(a) and m(b) respectively. In a level track, glider B has a spring-loaded plunger attached to it. At time t(i), glider A moves to the right with speed...

Hello everyone, I stuck on this problem: find the dimension of the space of dimension of the space of skew-symmetric bilinear functions on $V$ if $dimV=n$. I thought in this way, for skew-symmetric bilinear functions, $f(u,v)=-f(v,u)$, then the dimension will be $n/2$ Am I right? thanks

Hi all, I have the following program, but with this error [Subscripted assignment dimension mismatch. Error in test_vlf_spherical (line 62) ep(i,j)=ga(i,j)*ep(i,j)+gb(i,j)*((1./r(i)./dr)*(rph*hr(i,j)-rmh*hr(i-1,j))...] i am trying to solve the problem by using (./) but i...

I want sthg I can visualize in order to understand , I keep asking and am always told time , so how is time a 4th dimension ? I try my best but my mind is too weak to visualize things more complex than disney (so please , I want sthg in that standard ,consider me a curious 6 year old child)

I recently heard that it was found how gravity would behave in different dimensions of space. Apparently, while in our 3 dimensions of space gravity is F= x/r^2, in 4 dimensions it would be F=x/r^3, so it would be weaker, and in 2 dimensions it would be F=x/r so it would be stronger.What it...

I am studying scattering from these notes. There I came across Green's function in one dimension which is computed as \langle x|G_o|x'\rangle = -\frac{iM}{\hbar ^2k}\exp(ik|x-x'|) I understand Green's function as a sort of propagator from x' to x. There are two observations that can be made...

Homework Statement In the following expression x is a position and t represents time. What are the physical dimensions of each of the constants α and β? Also, for each what are the corresponding SI units? Homework Equations x=α+(2/3)βt^(3/2) The Attempt at a Solution I know that since x is...

Homework Statement Car A is located 43km away, 17 degrees north of west. Car B is 34km away, 38 degrees east of north. The person in car A checks the position of car B by using a GPS. What does it give for car B's a) distance from car 1 b) direction, measured due east? Homework Equations...

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How is the dimension of solution space is n-r, where n is the number of unknowns and r is the rank of A.

Hi, Using the definition of Hausdorff measure: http://en.wikipedia.org/wiki/Hausdorff_measure I am looking for a simple proof that Hd(C) is greater than 0, where C is the Cantor set and d=log(2)/log(3) Thank's in advance

Hey Guys, I, FYI not a physicist, recently got a fascination to dimensions, and for the life in me I can't seem to wrap my head around the fact that time is the 4th dimension. From what I can understand, the spatial dimensions can completely perceive the dimension below, but perceive an...

Homework Statement Consider the states with the quantum numbers n = l = 1 and s = 1/2 Let J = L + S What is the dimension of the Hilbert space to describe all states with these quantum numbers? Homework Equations The Attempt at a Solution I believe the dimension of the Hilbert...

Hi, I am trying to understand why do the two versions of Hausdorff (fractal) dimension are actually the same.I refer to the definition by coverings and the definition by ratio of two logarythms. http://en.wikipedia.org/wiki/Hausdorff_measure...

although the anthropic landscape looks appealing, I am not big fan of the string theory, due to untestable extra dimensions. In isolation, without sensory information(experiments) the humans(theoretical physicists) start to hallucinate(String theory). But what if higher dimensions can be probed...

Homework Statement A person takes a trip, driving with a constant speed of 94.0 km/h except for a 22.0-min rest stop. The person's average speed is 71.5 km/h. (a) How much time is spent on the trip? (b) How far does the person travel? This is for introductory general physics. We...

Hi, Can someone give me a link to a clear and relatively basic and short matirial introducing the notion of fractal dimension (Hausdorff dimension)? Thank's in advance.

hi all, i am new with fortran 90. i have here codes for 2d fdtd polar coordinates. but i have problem handling with increment in dimension in real number (as higlighted below). I have googled how to write the increment in do loops, but do loops only applicable for integer. can anyone help me...

Homework Statement Homework Equations \begin{align} \Delta p \Delta x &\geq \frac{\hbar}{2}\\ \langle p \rangle &= \sqrt{\langle p^2 \rangle - \langle p \rangle^2}\\ \langle x \rangle &= \sqrt{\langle x^2 \rangle - \langle x \rangle^2} \end{align} I allso know that a wavefunction of a...

Hello everyone once again. If I remember correctly, hypercubes are said to have 4th dimension. But as far as I know, the 4th dimension is time. So, when we're describing the 4th dimension I guess we can say, " Let's meet at my house at 12.20 pm". When I say "at my house" I'm talking about the...

So I had a discussion with my brother about this (it was sort of a joke, but I am a mathematician and every joke I turn into a theorem and vice versa... :-)), it was kinda of short. But if we already have dimensions which aren't whole integer numbers (he didn't know that, and didn't seem...

when we throw an object upwards why the time of descent is greater rhan time of ascent?

hi Riemann tensor has a definition that independent of coordinate and dimension of manifold where you work with it. see for example Geometry,Topology and physics By Nakahara Ch.7 In that book you can see a relation for Riemann tensor and that is usual relation according to Christoffel...

OK, I am working on proofs of the rank-nullity (otherwise in my class known as the dimension theorem). Here's a proof that my professor gave in the class. I want to be sure I understand the reasoning. So I will lay out what he had here with a less-precise layman's wording, as I want to be sure...

Let S be a subspace of $\mathbb{R^2}$, such that $S=\{(x,y):2x+3y=0 \}$. Find a basis,$B$, for $S$ and write $u=(-9,6)$ in the $B$ basis. So, I started to solve $2x+3y=0$ for $x$ and I got $x=-\frac{3}{2}y$. Then I could write, $\left[ \begin{matrix} x \\ y \end{matrix}\right] = \left[...

I know the trace tr[\gamma_5 a\!\!\!/b\!\!\!/c\!\!\!/d\!\!\!/] in 4-dimensional space-time, how is the result of it in D dimension? Is it the same as in 4 dimension?

Why are strings only one dimension? Why is the fundamental particle a one dimensional string as opposed to,for example, a three dimensional ball that oscillates?

I know little about this topic, yet it interests me beyond imagining. What can you guys tell me about it? Anything at all

The cartesian product ∏X = Xi of a countable family {Xi} of regular spaces is zero-dimensional i f and only i f all spaces Xi , are zero-dimensional. I wonder if the countability assumption is just to ensure the regularity of the product space ,or it is crucial for the clopen basis. Thank's

A differential equation of solitary wave oscillons is defined by, $$ \Delta S -S +S^3=0 $$ **How can we write this equation as,** \begin{equation} \langle(\vec{\nabla}S)^2\rangle+\langle S^2\rangle-\langle S^4\rangle=0 \tag{1} \end{equation} where $\langle f\rangle:=\int d^Dx f(x)$...

Though it may seem like it, this certainly isn't a homework question so I hope I don't offend anyone with it's placement. This is a simple drawing of a hydraulic mechanism that me and a friend are building. There is much debate about where we need to improve so we are leaving it up to you, the...

Define: $$\mathbb{Y} = C \times C^{c} \subset \mathbb{R}^{2}$$ where ##C## is the Cantor set and ##C^{c}## is its complement in ##[0,1]## First I think ##\mathbb{Y}## is neither open nor closed. Second, the Hausdorff dimension of ##C## is ##\Large \frac{log2}{log3}##. How do we...

Just finish watching hangout with cern.. Thats a part when the theorist explain abt conservation of energy that seems very vague. He explained that, with extra dimensions, we could observed that energy is not conserved. And he added that it might have relation to a lot of things, such as dark...

Just wondering why everything measurable in the universe appears in 3 dimensions?(as far as I know!) And why universe build up(objects) based on three dimensions ?is that anything to do with thermodynamic(Entropy)? Cheers,

Is there such a thing as a virtual dimension. for instance if you move on a two dimensional surface, say you take 4 steps in x dimension and then 3 steps in y dimension and then say in z 3 steps, and to move in z you step x+(some predefined formula) and y+(some predefined formula). The z...

Good Day! First of all, I'm not an actual physicist so please don't laugh if the following sounds really stupid to you or I don't use the correct terminology. I don't/didn't even study anything remotely related to physics, everything is plainly based on private interest. (The reason I'm still...

I don't really know where this topic belongs. Let's say you're an ugly asymmetrical person, with your right hand much larger than the left. A 4th dimensional being removed you and "flipped" you in the 4th dimesion, then put you back. Would you come back with a large right hand...

How is a dimension defined in quantum mechanics?

Homework Statement \lim _{ (x,y)\rightarrow (0^{ + },0^{ + }) }{ \frac { { e }^{ \sqrt { x+y } } }{ 4x+2y-5 } } Homework Equations eh. SO I did the problem. I usually sub 1/n for 0+ in most of these, but clearly the top goes to 1 from +inf, and the bottom goes to -5... Hence...