Dimensions Definition and 1000 Threads

Homework Statement A plane flies 600km/h south. The plane encounters a southwestern wind of 100km/h. Homework Equations What is the velocity (magnitude and direction) of the plane The Attempt at a Solution What I did was break the 100km southwestern vector into its components. 100*cos45 =...

What are the mathematics behind multiple dimensions? Does mathematics allow for the existence of more than four dimensions? What allows the ability to possesses more that four dimensions, if there is already proof? I looked around, but I didn't find much by way of the answer I was looking for.

The Galilean transforms for rotations, boosts and translations in 2D are the follows: Rotations: x' = xcosθ + ysinθ y' = -xsinθ + ycosθ Boosts: x' = x - vxt y' = y - vyt Translations: x' = x - dx y' = y - dx I wanted to combine these into a single pair of equations, so my first thought was...

I am interested in the derivation of the inverse square law in various dimensions via Green's functions. I think the trick is to imagine a sphere and then to integrate over it. Does anyone know a book or notes where this is explained? I found this below from here, but could not really...

Complex numbers ##a+bi## can be thought of as a second dimension extension of the real number line. Is there a third dimension version of this? Are there even more complex numbers that not only extend into the y-axis but also the z axis? tex

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...

Homework Statement Show that if v(x,t) and w(y,t) are solutions of the 1-dimensional heat equation (v_t = k*v_xx and w_t = k*w_yy), then u(x,y,t) = v(x,t)w(y,t) satisfies the 2-dimensional heat equation. Can you generalize to 3 dimensions? Is the same result true for solutions of the wave...

In a linear accelerator that use cavities and microwaves or radio waves to accelerate particles, how would one find dimensions such as cavity openings, cavity size, length between cavities, etc.

I am following up my 8 years old daughter's homework, and want to show her how division and multiplication work together , such as in division by a fraction : am I right if I say " we divide chocolates by boxes and 6 chocolates divided by half a box means 6 x 2 half boxes = 12 in one box ? " or...

Hello all I hope you can help me with this query. I would like to find an introductory text in extra dimensions. I am taking a course in BSM and I have been referred to: C. Csaki, TASI lectures on extra dimensions and branes, hep-ph/0404096, but I was hoping to find something more...

I am a programmer trying to simulate some 2D balls bouncing about and colliding with each other. I have both the ball's velocity components before the collision and I am trying to solve for them. I went to wikipedia to find a formula to satisfy my needs and ran into this section...

I couldn't finish it, so I paid $35 for Alan Macdonald's Vector and Geometric Calculus. This uses geometric algebra, where vectors may be multiplied together to form bivectors, trivectors, and so forth. They are added together with abandon. The electric field E is more or less 1D so it is...

first i would like to ask a question .. imagine there are 2 dimensional creatures that are able to live and interact . they can exist in the second dimension with no problems . can the surface of a sphere precieved as a valid 2 dimensional space that these creatures can exist in ?( if yes then...

Homework Statement Given the linear transformations f : R 3 → R 2 , f(x, y, z) = (2x − y, 2y + z), g : R 2 → R 3 , g(u, v) = (u, u + v, u − v), find the matrix associated to f◦g and g◦f with respect to the standard basis. Find rank(f ◦g) and rank(g ◦ f), is one of the two compositions an...

Is there an alternative set of equations similar to Lorentz Transformations that transforms vectors from one dimension to a higher or lower dimension?

I am self learning Physics From a course I read the following : " .. d^2x/dt^2 = -k/m x The left hand side is an acceleration so k/m must have dimensions of (time)−2 .. " I understand that the left hand is acceleration but why does it imply that k/m must have dimensions of (time)−2 ? I...

I am reading the proof of the Riemannian Penrose Inequality (http://en.wikipedia.org/wiki/Riemannian_Penrose_inequality) by Huisken and Ilmamen in "The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality" and I was wondering why they restrict their proof to the dimension ##n=3##...

I asked my teacher , i didnt get any satisfactory answers , can u tell me why dimensions are always at right angles .

Hello, Surfing across the internet, I learned that the volume of a sphere in n dimensions can be expressed by V(n) = (Π^(n/2)) / Γ((n/2)+1), where n is the number of dimensions we are considering But if we consider n=0, then we get 1. So, how do we interpret this? I mean what does volume in zero...

I think I've read the the tensor in three dimensions has 10 elements in its matrix(?). Is this related to the 10 dimensions in some forms of string theory?

hello, I'm designng a f1 car,,, we are using a duke 390 engine...we are using a chain differential... now I'm trying to make the sprockets. to make this sprockets i need to know its dimensions.. that is sprocket teeth diameter width etc... so, I'm very much confussed with it. how to get this...

how dimensions of differential are made with respect to engine power and torque

I want to discuss here a very unusual idea that many "serious" theoretical physicists don't want to discuss, but I think it is time for such a discussion, because many things in mathematics for physics have changed in the last 10 years. When we calculate in chiral scalar superfields then we get...

Homework Statement The electric field between two circular plates of a capicator is changing at a rate of 1.5 x 10^6 V/m per Second. If the displacement current this instant is ID = 0.80 x 10^-8 A find the dimensions of the plates Homework EquationsThe Attempt at a Solution The capacitance of...

I know modern physics theories make use of really high number of spatial dimensions, I wonder how relevant these high dimensions are for physics. I am only a guy from High school interested in physics, but I would like if possible a formal answer

string theory predicts dimensions but predicts 10 dimensions. Penrose twistor theory correctly predicts 4 dimensions, doesn't this make it more successful?

It's my understanding that, if we ignore the temporal dimension and just focus on spatial ones, then you get to the third dimension by starting with a point and adding perpendicular lines to them. Once you've done this a couple of times, you get three dimensions. Obviously, to the layman, it...

Hello! (Wave) I have written the following code in matlab: function v=uexact(x,t) v=sin(2*pi*x)*exp(-4*pi^2*t); end function [ex]=test3 h = 1/50; T=1/2500; x=0:h:1; t=0:T:1; ex=uexact(x,t); end I...

A 2-dimensional creature living on the surface of a 3-dimensional sphere could conclude he lives in a finite, unbounded universe. Is it necessary for a 3-dimensional creature to assume there is a 4th spatial dimension in order to conclude the universe is finite and unbounded? I have seen a...

According to general relativity, time is a dimension, one of four dimensions that form 4D spacetime - a structure which is mathematically symmetrical and homogeneous. Should not all four dimensions, therefore, be mathematically interchangeable? Assuming that we are 3-dimensional bodies...

Large Extra Dimensions I watched a video with Brian Greene explaining string theory and he said that extra dimensions may be curled up very tiny and that's why we don't see them. Is it possible that some extra dimensions may be very large but we don't see them or are all of them very tiny?

Hey guys! After watching another awesome video of minutephysics: I couldn't help but wonder, what is a dimension? Thanks for your replies in advance,

Homework Statement The frequency of a simple pendulum depends only on its length and the gravitational field strength. Use dimensions to derive a possible form for the equation for this frequency. Homework Equations [/B] Not sure. I was looking at f = 1/T as a starting point and g = F/m The...

Despite the similar nature of charges,protons remain inside the nuclear dimension.why?

Homework Statement Homework Equations ∫F⋅dr=W The Attempt at a Solution

It statics, I am having difficulty on getting perfect to read the dimensions correctly in order to find the forces! This photo for example I put B = (-3i,-2j, -6k) but correct answer is (3i,-2j,-6k) ... why 3i but not 3i ?! I'm reeally confused For C I put -1i but correct answer is 3i...

Hi, Gleason's theorem fails if the dimension of the Hilbert space is two. Does this allow for violations of Born's rule in two-dimensional systems? Or can you somehow tensor the system with the (ever-present and infinite-dimensional) Hilbert space of the rest of the universe, apply Gleason's...

Can I get the derivation of the dimensions of the physical quantity ELECTRIC RESISTANCE which is given by :- A simple derivation is only required. Thanks in advance.

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...

1. Homework Statement (The following is taken from Sears and Zemansky’s University physics with modern physics, thirteenth edition by Young Freedman. Chapter 3 bridging problem: Launching up an incline at page 95. You fire a ball with an initial speed ##v_0## at an angle Φ above the surface...

I have to calculate the optimal dimensions for a cylinder of this volume, if the amount of materials used to build it is to be kept to a minimum. The volume of the cylinder is = 498.76cm^3 THIS IS WHAT I HAVE SO FAR, V= pi R^2 , h= 498.76/pi R^2 S.A =2piR^2 + 2piRh = 2piR^2 +...

Consider a block of a piezoelectric material sandwiched between two parallel plate conductors, sort of like a parallel plate capacitor with a piezoelectric material as its "dielectric." If applying the same pressure to two of these configurations, does the thickness of the piezoelectric block...

Halo, I was reading about geometry from Tim Gowers book titled "A very brief introduction to mathematics". I came across fractional dimensions and the 4th dimension. The koch snowflake has dimension 1.2 yet he could comfortably drawn it on a 2d page (or is it complete?). Has not he just...

Say a ring is spining around the z-axis, an angular impulse is then applied to it in the x-axis, what is the resultant motion qualitatively and quantitatively? How can it be calculated? (You can make up the quantity of z-angular momentum and x-angular impulse)

Homework Statement hello guys, that's the problem, when i tried to solve it using soh cah toh and Pythagoras law it resulted in answers e' and f', which make sense to me because both result it 54.6N and both relevant in directions so i am a bit confused.[/B] Suppose that a force with a...

A two-dimensional surface with everywhere positive curvature is a closed surface with no boundary (isomprphic to a sphere). Is this true for higher dimensional surfaces as well? Would a three-dimensional surface, with everywhere positive curvature be a closed hypersurface isomorphic to a...

I want a closed two dimensional manifold embedded in four dimensions. Is the following way a good one : Parametrize a 3 sphere with $$\theta,\phi,\chi$$ Put $$\chi=f(\theta,\phi)$$ Does it make the manifold closed ?

I know what imaginary numbers are, but I'm struggling to understand why the Lorentz transformation makes a time-like dimension space-like. I suppose what I'm really asking is what is the difference between time-like and space-like. I've read that it has something to do with special relativity...

Strings are said to be one dimensional, due to the math. And I understand that there are problems in the math when they put the strings in 3 or 2 dimensions. According to string theory, lengths smaller than Planck length have no physical significance. Could it be that strings are 3...

In four dimensions, left and right chiral fermion can be written as \psi_L= \begin{pmatrix} \psi_+\\ 0 \end{pmatrix},\qquad \psi_R= \begin{pmatrix} 0\\ \psi_- \end{pmatrix}, respectively, where \psi_+ and \psi_- are some two components spinors(Weyl spinors?). In this representation, the...