Dimensions Definition and 1000 Threads

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...

A typical demand function is y=5000-p where y is quantity demanded and p is price. But this equation isn't dimensionally correct. What am I missing?

I do apologize if this is the wrong place to post this. Why is it necessary to have 11 dimensions in M Theory? I've been at it for days emailing universities, Twitter, etc. No one has attempted to give me an answer and it's frustrating me. I just want to know what the purpose of each of the...

<<Mentor note: This thread has been split from this thread due to going a bit off-topic.>> I would actually disagree with this. Any tensor has well defined units, but its components may not have the same units as the tensor basis may consist of basis tensors with different units. For example...

I hope I'm asking in the right forum. I'm trying to understand the subject of more dimensions a little better. Does the dimensions predicted by string theory have to be small? Can our known dimensions predicted by string theory actually be inside much larger dimensions?

Question: In an anniversary celebration of Marilyn Bell's 1954 feat- she was the first person to swim across Lake Ontario- a swimmer set out from the shores of New York and maintained a velocity of 4m/s (N). As the swimmer approached the Ontario shore, she encountered a cross-current of 2 m/s...

String theorists postulate that our world has 9 dimensions and these extra dimensions are very twisted up such that they are too small to be seen. Question 1: Why don't we postulate, instead, that the reason we can't see these extra dimensions is because we are not genetically wired to do so...

This is the link to the relevant paper. I have to show that vector (t', x', y', z') lies on the sphere. But for that to be, V^2 has to be 1 according to the equation in the introductory part of the section 2. That, by definition, means that E=-m/2. What does that mean, and why is this solution...

Problem This is a conceptual problem from my self-study. I'm trying to learn the basics of group theory but this business of representations is a problem. I want to know how to interpret representations of a group in different dimensions. Relevant Example Take SO(3) for example; it's the...

The closure relation in infinite dimension is : ∫|x><x|dx =I (identity operator),but if we apply the limit definition of the integral the result is not logic or intuitive. The limit definition of the integral is a∫b f(x)dx=lim(n-->∞) [i=1]∑[i=∞]f(ci)Δxi, where Δxi=(b-a)/n (n--.>∞) and...

Homework Statement A particle with mass m can move freely in three dimensions. Explain why the stationary states of the particle are determinate states for angular momentum (L_z and L^2) Homework Equations L^2 = L_x^2 + L_y^2 + L_z^2 L = r \times p \hat{H} =...

In the links below Carl Sagan and TED-Ed described about higher dimension: and here's a description of Brian Greene: Carl Sagan and TED-Ed explained, we can not see the higher dimensions because we are limited to perceive only three dimensions. They didn't say a dimension can be small or...

Hi guys, I'm a high school senior currently in calculus and vectors. We're in our application unit right now, and I'm having quite a bit of trouble with problems that give the desired volume/area, and then ask you for the minimum dimensions required for said volume. One notable problem that I am...

Homework Statement Prelim: my question is about a very specific part of a question whereby the student is asked to derive the final formula for the general solution in two vars, but I will post the entire question for clarify. Newton's Method for approximating the roots of an equation f(x)=0...

We know that the 3+1 dimensions all fit together in a nicely with Lorentz covariance. We can rotate and apply Lorentz boosts without breaking the laws of physics. How do string theory's extra dimensions fit in with this? Does it make sense to rotate between a normal space dimension and one of...

Homework Statement [/B] Let α ∈ ℂ be a complex number. Let V = ℚ(α) be the rational vector space spanned by powers of α. That is ℚ(α) = <1,α,α2,...>. 1) If P(t) is a polynomial of degree n such that P(α) = 0, show that dimℚℚ(α) is at most n.Homework EquationsThe Attempt at a Solution...

Let α ∈ ℂ be a complex number. Let V = ℚ(α) be the rational vector space spanned by powers of α. That is ℚ(α) = <1,α,α2,...>. 1) If P(t) is a polynomial of degree n such that P(α) = 0, show that dimℚℚ(α) is at most n.Here is my attempt to solve this question. Please give me some...

Homework Statement I need to find velocity v from the drawing. Homework Equations Equations of kinematics The Attempt at a Solution I found that v=12.134 m/s . I need to know is it correct. [/B]

I was supposed to measure a beam at a far away worksite but after a series of unfortunate events, I wasn't able to. All I know at the moment is it is referred to as I55 beam. I searched for it using every combination of words I can think of but cannot find it. We normally don't use beam...

Homework Statement a boy on whom the force of gravity is 400 N hangs on to the middle of a rope stretched between two trees. The rope sags in such a way that it makes an angle of 170 degrees at the boys hands. what force does the rope exert on each tree? Homework Equations F=ma The Attempt at...

Homework Statement The electric field between two circular plates of a capacitor is changing at a rate of 1.5 x 10^6 V/m per second. If the displacement current at this instant is Id = 0.80 x 10^-8A, find the dimensions of the plate. Homework Equations Id = ΔQ/Δt = ε0(ΔΦE/Δt) ΦE = EA Q = CV...

Homework Statement Find the arc length of r(t)= <tsin(t), tcost(t), 3t> from 0 to t to 2pi (inclusive) Homework Equations Integral from 0 to 2pi of the magnitude of r'(t) dt The Attempt at a Solution 1. Must find the derivative of the function. Using the product rule a few times, the...

Homework Statement A soccer ball is kicked from the ground at an angle of 30◦ with speed 30m/s. Determine the duration of the flight, range and maximal height of the trajectory. Homework EquationsThe Attempt at a Solution 1. Break down the velocity vector into x and y components: 30cos(30) =...

I was wondering if I can expand the FRW metric in d spatial dimensions, like: g_{\mu \nu}^{frw} = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & - \frac{a^2(t)}{1-kr^2} & 0 & 0 \\ 0 & 0 & - a^2(t) r^2 & 0 \\ 0 & 0 & 0 & -a^2 (t) r^2 \sin^2 \theta \end{pmatrix} \rightarrow g_{MN} = \begin{pmatrix} g_{\mu...

Homework Statement A frightened rabbit runs onto a large area of level ice that offers no resistance to sliding, with an initial velocity of 6m/s toward the east. As the rabbit slides across the ice, the force of the wind cases it to have a constant acceleration of 1.4 m/s^2, directed due...

please point out the flaws/add to my reasoning here: it is known that energy is quantized, but could that be for just the 3 dimensions we're able to experience? Is it illogically to propose that energy might not be quantized when looking at all of the dimensions together? this could explain...

Homework Statement r(t) = <cos(t), 2t, sin(t)> from 0 to 2pi (included). Compute the integral from 0 to 2pi of r(t). Homework EquationsThe Attempt at a Solution [/B] We haven't learned this in class yet, so I am getting a head. My idea is to simply put r(t) in and integrate term by term so...

In the process of descending from a higher dimension to a lower one, there must be more than one factor that could not be solved (or descend.) My little own experiment.. http://mr-none.meximas.com/public_html/pic/1.JPG Steps: 1, wrap a plastic bag around a basketball. 2, draw a "triangle" with...

So, I have some questions regarding 'dimensions' and 'parameters' in physics. (there are differences in the meaning between physics and mathematics, as far as I understand it) ---- As far as I understand it, we live in a 4-dimensional world, consisting of 3 space and 1 time dimensions. Yet we...

I understand the theory of special relativity and the mathematics which support it. I even understand that the time dilation has been proven. Therefore I am going to ask a question which on first blush may appear that I disagree with it but that is not the case. The question I can not seem to...

Homework Statement A freight train is moving at a constant speed of 10 m/s. A man standing on a flatcar throws a ball into the air and catches it as it falls. Relative to the flatcar, the initial vellocity of the ball is 15 m/s straight up. a. What are the magnitude and direction of the...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > A balloon going upwards with a velocity of 12 m/s, is at a height of 65m from the Earth at any instant. Exactly at this instant a packet drops from it. How much time will the packet take in...

So I was watching this video on Khan Academy, and it talks about graphing functions that have values in multiple dimensions. It shows how to represent a linear function in 3 dimensions with a set of vectors, L ={p1 + t(p1-p2)|t∈R} where p1 and p2 are vectors that lie on the line you want to...

I am working through an explanation in Nielson and Chuang's Quantum Computation book where they apply a CNOT gate to a state α|0>|00> + β|1>|00>. (The notation here is |0> = the column vector (1,0) and |1>=(0,1), while |00> = |0>|0>, and |a>|b>=|a>⊗|b>, ⊗ being the tensor (outer) product. I am...

Gorini 1971 (reference below) proves a no-go theorem for attempts to extend the Lorentz group to superluminal velocities in n+1 dimensions, for n\ge3. His assumptions are stated in abstruse notation, but he gives the following translation into plainer language: > Axiom: [...] time has a...

Homework Statement Index exceeds matrix dimensions Homework EquationsThe Attempt at a Solution I am trying to output into a text file something like this: Name ID scE ccE scC ccC Fake Subject 1 1 3 4 5 2 Fake...

Hello there, I have a confusion between dimensions and units! All of others tell me its not unit but some use units! Please verify the following Quantity Dimension Length L Mass M Time T Temperature Θ Amount of...

I have considered the possibility that dark matter is so hard to find because it exists in extra dimensions. Before posting here I googled this, and found that some scientists postulate this exact possibility, while others consider that extra dimensions themselves cause the effects that are...

Homework Statement This isn't exactly a HW question, it's a question in my statics midterm today, he wants the reactions at the supports B and C, which is easy but the problem is this 60 N.m moment, all my friends were like :" let's just sum the moments around B ( due to the 50 N and the...

Homework Statement We want to build a micro-positioning system that produces a maximum travel of 5 μm by using a piezoelectric linear actuator beam with a square cross section (a^2) and length (l) as shown below. A piezoelectric material with piezoelectric coefficients d13 = -2.0×10-8, d33...

Have fun: Art, Ben, Cam, Dan and Ern each added a different kind of room to his house. Each added room can have a width of 10, 11, 12, 13 or 14 feet, and a length (not necessarily respectively) of 15, 16, 17, 18 or 19 feet. From the clues below, determine the kind of room each man added as...

Hi guys, So I have the following Lagrangian: \mathcal{L}=\bar{\psi}(i\partial_{\mu}\gamma^{\mu}-m)\psi+\frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi)-\frac{M^{2}}{2}\phi^{2}-\lambda\bar{\psi}\psi\phi where m is the is the mass of the spin-half Dirac field and M is the mass of the spin-0...

hi guys, i am new here, not even sure this is right place to put this questions, I always understood time as a 4 dimension, just a diferent reference when compared with x,y and z. but is it possible that we r trying to see it in a different way? is it possible that time itself have its own x y...