Dimensions Definition and 1000 Threads

Homework Statement Let Pn denote the linear space of all real polynomials of degree </= n, where n is fixed. Let S denote the set of all polynomials f in Pn satisfying the condition given. Determine whether or not S is a subspace of Pn. If S is a subspace, compute dim S. The given condition if...

Is there an intuitive reason or proof demonstrating that in general dimensions, there is no direct analogue of the binary cross product that yields specifically a vector? I came across Wedge Product as the only alternative, but am just learning linear algebra and don't quite comprehend yet...

Homework Statement Let \vec{F}=2\hat{i}-3\hat{j} act on an object at point (5,1,3). Find the torque about the point (4,1,0) Homework Equations \tau = \vec F \times \vec r The Attempt at a Solution Please tell me if my procedure is correct. Let the object occupy point A at (5,1,3) and let...

It is frequently stated in the literature that the first attempt to unify gravitation and electromagnetism through a theory in higher dimensions was attempted by Kaluza and Klein. Yet, today I have realized that this is not true. The first such attempt was done by Nordstrom in 1914...

Hi everyone. I can not remember if, in 3D, the higher it is the energy level, the higher it is its degeneracy. With a cubic well and with a 3D harmonic oscillator it holds... Does anyone know if it is a general rule or not (and in the case it is, where does this rule come from)?

Recently, I learned that, in a probability density function, the probability of the occurrence of any specific x-value is in fact zero, for the relevant interval on the function is a point, which has zero width and therefore has zero area associated with it under the probability curve. This...

question stated in title. Thanks!

In its broadest sense, quantum entanglement means that two 'particles' separated by distance, and moving away from one another, behave as if they are next to one another. In a mental experiment, you can imagine what the world might look like to these two particles as they zoom away from one...

I am pretty sure this question must have been asked before... However I was always wondering, what would a theory be like if we allowed to have two time-dimensions (so I think a SO(2,3) symmetry). In general this would allow time-rotations / rotations of the arrow of time, so I guess the light...

I've been reviewing the timeline of the big bang... http://en.wikipedia.org/wiki/Chronology_of_the_universe http://en.wikipedia.org/wiki/Graphical_timeline_of_the_Big_Bang ...and wasn't able to find an answer to a question I have. That question is, is there any evidence that the...

I am currently working on an assignment using Tanagrams. I have the information that I have: • 2 large, and congruent, isosceles right triangles • 1 medium isosceles right triangle • 2 small, and congruent, isosceles right triangles • 1 square • 1 parallelogram The pieces can be...

I'm trying to explicitly show that \varepsilon^{0 i j k} \varepsilon_{0 i j l} = - 2 \delta^k_l I sort of went off the deep end and tried to express everything instead of using snazzy tricks and ended up with \begin{eqnarray*} \delta^{\mu \rho}_{\nu \sigma} & = & \delta^{\mu}_{\nu}...

Need some help reading these dimensions, they're from a draft made in catia v5

I know this is far from what a strict obeyance to the principle of occoms razor may result in and its probably wrong. is it theoretically possible that as a star contracts to result in a black hole, the contraction does not stop when its just a point hole, but continues, expanding in a negative...

I am sorry, this is a rather dump question- more like a notation question since the sources I've looked into don't specify it... But in case I want to calculate (in general dimensions) the: \Gamma^{2}_{chir} =1 Do I have to take: \Gamma_{chir} \Gamma_{chir} or \Gamma_{chir}...

I've seen a lot of the popular theories regarding how many dimensions there are, and it seems that they all have numerous spatial dimensions and one dimension of time. However, I haven't really found out much about why there is only ever a single dimension of time in any given theory. While I...

I've heard that extra dimensions can be (due to gravitational experiments) of dimensions ~some millimeters... I'm quiet skeptical about this issue... Why would someone choose gravity (such a weak force for those experiments) to determine the scale? why not use Electromagnetism , that has...

If I understand it, Hilbert spaces can be finite (e.g., for spin of a particle), countably infinite (e.g., for a particle moving in space), or uncountably infinite (i.e., non-separable, e.g., QED). I am wondering about variations on this latter. The easiest uncountable to imagine is the...

Is the Higgs field 4 dimensional?

Anything that exists has to exist/interact with at least 4 dimensions, right? Stuff existing/interacting with other dimensions too (even if they can't be/haven't been observed) have to exist/interact with our 4D as well, right?

I have heard of Flatland and seen many analogies regarding a 2 dimensional world but, can such exist? Considering that even subatomic particles move in 3 dimensions then am I to assume that a 2 dimensional world is an impossibility? Even a line is 3 dimensional for if a line were only 1...

Homework Statement The Attempt at a Solution Can someone please check my work?

Hi all, I am trying to calculate the damping coefficient of a linear viscous dashpot/damper given the dimensions of the piston, and the dynamic viscosity of the damping fluid. I have found this calculator, but does anyone know the equation that it uses...

A homeowner wants to fence a rectangular play yard using 72 ft of fencing. The side of the house will be used as one side of the rectangle. Find the dimensions for which the area is a maximum and determine the maximum area. I got L=18 and W=36 So my maximum area is 648 ftIs this correct?

I've come to the point in my homework discussing the above, and more specifically, energy levels, wave functions, excited states etc.. And while I can locate an appropriate formula and plug-n-chug, I'm finding that I have no clue what these equations and numbers actually mean. And(in my...

I'm doing practice problems: I am confronted to this: The dimensions of force are (x means “multiplied by”): (a) kg.m.s-2, (b) mass x length x (time)-2, (c) Newtons, (d) mass x acceleration. I need someone to back up my reasoning. It says dimensions, so I'm going towards (b)...

Motion in two dimensions! Help! Homework Statement The coordinates of an object moving in the xy plane vary with time according to the equations x =-5.00 sin (vt) and y= 4.00 - 5.00 cos (vt), where v is a constant, x and y are in meters, and t is in seconds. (a) Determine the components...

The Children at Tiny Tots Day Care plant a rectangular vegetable garden with a perimeter of 210m. The length is 3/4 the width, Find the dimensions of the garden. I have no idea how to set up an equation. Any help is appreciated. Would it be like 210=2(3/4+x)? or 210=2(x-.25)?

Hey Guys! To begin with, I apologize if I am using the wrong terminology. I've just begun learning about linear algebra. So I was working on a problem in the book "Introduction to Linear Algebra" by Gilbert Strang, fourth edition (problems 9 and 11 on p. 8). Problem 9: If three corners of a...

3) Calculate the dimensions of the straight circular cone, smaller volume that can be circumscribed around a cylinder of RADIUS "R" and height "H". Answer is h = 3H and r= 3R/2

I understand that we live in a 3D world. X,Y,Z...Up-Down, Left-Right, Frontwards-Backwards. But I hear theoretically ideas of the 4th dimension, time? As well as String Theory with as many as 11-dimensions. Are any of these higher/lower dimensions provable? And is the 4th dimension that is...

I often read about the weakness of gravity being explained by gravity leaking into extra space dimensions. But, if there is a large 4th space dimension that only gravity can access, that would make gravity follow an inverse cube law. Observation clearly shows an inverse square law that Newton...

Homework Statement I know that intensity is power per unit area. When I do a dimensional analysis, it reduces down to mass per cubic time. Is there any physical significance to that? Homework Equations I=P/A The Attempt at a Solution

Homework Statement Hi, I have to do a simulation of two non linear dynamical equations which represent a electromechanical system. (An inverted pendulum attached to a cart moving over a rail). I am going to simulate the response via numerical methods programmed in LV. (I am trying firts with a...

I recently heard one theory of parallel universes simply being extra dimensions (one thing string theory requires I believe). Well I also happened to be thinking about quantum entanglement. It is still unknown how this phenomenon works right? Well I had this idea that I suppose can't be...

Homework Statement Two objects, Red and Blue, are in inertial motion with respect to each other and are graphed on the attached Minkowski diagram (representing a third inertial frame). Red and Blue are in relative motion along the x axis, and offset slightly on the z axis such that they...

Homework Statement Find the vector equation for a line segment from (2,-1,4) to (4,6,1). Homework Equations Arithmetic :p The Attempt at a Solution What I did was that I simply solved for the distance between the two points and used it as my vector, I then said <4-2t, 6-7t...

This question mixes the fantastical notion of a force field with some down to Earth mathematics, and it’s the latter I need help with please! Assuming the following: • a truly huge force field capable of shielding a continent, i.e. along the coastline, • it is visible as a coloured...

Homework Statement Two thin rods are fastened to the inside of a circular ring as shown in the figure below. One rod of length D is vertical, and the other of length L makes an angle θ with the horizontal. The two rods and the ring lie in a vertical plane. Two small beads are free to slide...

I would like some information concerning GR and the dimensional contraction of a standard rod due to gravity. As the potential energy per unit mass decreases as one approaches the center of a planet, time dilates and therefore, space needs to contract, relative to one in deep space. I’ve seen...

Is it correct to state that if a space E has dimension 3 then: E = ℝ^{3} and that the two spaces are isomorph?

Homework Statement Two tugboats are pulling a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s? http://imgur.com/GS7Y80x Homework Equations c^2=a^2 + b^2 -2ab cosC sin A/ a= sin...

Hello Homework Statement An open tank is constructed with a square base and vertical sides to hold 32m3 of water. Find dimensions of the tank if the area of the sheet metal used to make it is to have a minimum value. Homework Equations The Attempt at a Solution I'm not...

Homework Statement Find the density of states g(ε) for an ideal quantum gas of spinless particles in dimension d with dispersion relation  ε= α|p|s , where ε is the energy and p is the momentum of a particle. The gas is confined to a large box of side L (so V = Ld) with periodic boundary...

OK, I think I am missing something very basic... When regularizing phi^3 theory in six dimensions, Srednicki comes to eq 14.30, which shows that the 1-loop contribution to the propagator diverges (the gamma function has a pole). This is good. OK. Now let d=5 (or epsilon=1). Actually, go...

dimensions -- how many are there in universe? how many dimensions are there in universe and what are they ?

Can the laws of physics work with any number of dimensions (whether they be space or time)? That's what Lisa Randall claims, but am seeking clarity. If so, does that mean Quantum Mechanics will still predict the same results in 5 or 6 dimensional universes, and the equations will stay the...

Qhy does SO(n) have the same number of dimensions of O(n), whereas SU(n) reduces the dimensions of U(n)? Isn't the constraint the same for both cases, i.e. detM=1?

Hi I have realized that I am horrible at setting up integrals in three dimensions when working with Coulomb's law (F = k q*∫r-2dq ). I don't have the vaguest idea how I can solve this using it and the superposition principle: I am not asking for a solution to this exercise. I want a good...

In this formula, E = 1/2 mv² 1/2 is not considered as it does not have any dimension. But then does it not affect the formula. Why? Explain! Please