Surfaces Definition and 425 Threads

I am not a mathematician but I have noticed how strangley similar the treatments of curvature and residues are when you compare the residues of residue calculus and the curviture of the gauss bonet forumlation of surfaces. Is there some generalization of things that contains both of these...

Homework Statement A given system has the equipotential surfaces shown in the figure . http://session.masteringphysics.com/problemAsset/1122530/1/Walker.20.39.jpg A)What is the magnitude of the electric field? B)What is the direction of the electric field? (in degrees from the +x...

Homework Statement Find the maximum and minimum values of f(x,y) = (xy)2 on the domain x2 + y2 < 2. Be sure to indicate which is which Homework Equations I am not sure what to put here. I solved this problem a different way, and I am not confident I did it correctly. The Attempt at a...

I'm completely confused with patches, which were introduced to us very briefly (we were just given pictures in class). I am using the textbook Elementary Differential Geometry by O'Neill which I can't read for the life of me. I'm here with a simple question and a somewhat harder one...

In this thread, I plan to try to explain (with some apropos ctensor examples) in a simple and concrete context some basic techniques and notions about Riemannian two-manifolds which also apply to general Riemannian/Lorentzian manifolds. Suppose we have a euclidean surface given by a C^2...

Homework Statement A given system has the equipotential surfaces shown in the figure What is the magnitude of the electric field? What is the direction of the electric field? (degrees from + x axis What is the shortest distance one can move to undergo a change in potential of 5.00...

Hi I've been drawing surfaces in Mathematica but some of the images come out jaggy and very unsmooth. Is there a command that can be added that will increase 'resolution' or smoothness of the surfaces. Thanks

Homework Statement Find the tangent vector at the point (1, 1, 2) to the curve of intersection of the surfaces z = x2 + y2 and z = x + y. Homework Equations The Attempt at a Solution I haven't started the problem, because I'm not sure what the first thing to do is. Do I have to parametrize...

How do I find this?

My textbook notes that if: \frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}}=1 and a \neq b \neq c Then the ellipsoid is not a surface of revolution. It seems to me though that one can always find a curve in the plane, which when rotated around a line will produce the...

Homework Statement A conducting wire carrying a charge \lambda per unit length is embedded along the axis of the cylinder of Class-A dielectric. The radius of the wire is a; the radius of the cylinder is b. Show that the bound charge on the outer surface of the dielectric is equal to the...

Homework Statement A set of concentric hemispherical surfaces is given, each of which is an equipotential surface. These concentric surfaces do not, however, have the same value of potential, and the potential difference between any two surfaces is also not constant. The surfaces are spaced...

Do dark surfaces exposed to the sun really contribute to global warming?

Hi all, I'm quite new here, but it's been a while since I've been browsing through these forums for past answered questions for calculus and physics, but now comes the time where I'm the one needing help that's not been questioned yet. Homework Statement Find some* vector funcion r with...

Here is the problem exactly how it is written on my paper... Consider the surfaces x^2+2y^2-z^2+3x=1 and 2x^2+4y^2-2z^2-5y=0. a. What is the name of each surface? b. Find an equation for the plane which contains the intersection of these two surfaces. That is the question. For...

A couple of pictures to get started: I'm not a physicist, but a professional artist, so an overly technical explanation may not have any meaning (especially if it's maths!). However I am very interested in how light interacts with matter and I am puzzled as to what is going on here...

Homework Statement Homework Equations f(x,y,z,)=(x-2)2+y2+z2 The Attempt at a Solution

I need help with developing a good understanding of equipotential surfaces corresponding to regions of three dimensional electric fields. I would appreciate if someone could refer me to a site or sites where this is comprehensively explained along with illustrations and with related conceptual...

Homework Statement Use parametrization to express the area of the surface as a double integral. tilted plane inside cylinder, the portion of the plane y+2z=2 inside the cylinder x^2+y^2=1 Homework Equations the area of a smooth surface r(u,v)=f(u,v)i+g(u,v)j+h(u,v)k a<=u<=b...

Try drawing this mentally: Start with a circle of radius r, draw n number of points spaced evenly on the circle. at each point on the circle draw another circle of radius r, once again with n number of points. What sort of a picture would one get repeating this process a million times, and as n...

Homework Statement A box is given an initial velocity of 5m/s up a smooth 20 incline surface . The distance the box travel before coming to rest is? Homework Equations I can't solve it correctly , I can't get the idea of this question The Attempt at a Solution x= ? vi=5 v=0...

Do the balls in a bearing actually touch both races? If so, how does the thing turn? Won't the balls be moving in different directions at each race, and therefore dragging against one?

okay i came up with doing the gradient of the ellipsoid. Then set that equal to the vector, <4,-4,6>. I solved and got x,y,z = 1,-2,1 I looked at the answer key and it said (1/3) (1,-2,1) Does anyone know where the 1/3 came from?

Homework Statement Given the surface: x^2 + y^2 + z^2 = 1 but x + y + z > 1 (actually greater than/equal to) I'd like to parametrize both this portion of the sphere and I'd like to find a parameterization of the boundary of the surface (that is, the intersection of the above sphere and...

If there's a point charge at the origin, I want to find two closed surfaces such that the flux through one of them is zero while the other is not. I know this may seem trivial but I just want to make sure I understand the question. My answer would be that to get a zero flux, the closed...

Hello guys. Is this even a valid question? Just curious. Thanks,

[FONT="Comic Sans MS"]light doesn't require a medium to travel ...but , then why can't light penetrate all surfaces??

I know that \int_{S}^{}\int_{}^{}\vec{B}\cdot d\vec{A} = 0 because \textbf {div} \vec{B}=0 IE, because \Phi_{B} leaving a closed surface must equal \Phi_{B} entering. Yet how is it then that \int_{C}^{}\vec{B}\cdot d\vec{l} isn't also equal to zero? Shouldn't it be true for any...

Is it true that the surface of a (hyper)cube in Rn is homeomorphic to Sn-1? Or only for particular n?

A beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction n. (a) If a point image is produced at the back of the sphere, what is the index of refraction of the sphere. Here's the equation you use to find the index of refraction of the sphere...

Homework Statement (i) Explain why it would not be possible to write the magnetic Field (B-field) in terms of a vector potential (A) IF magnetic monopoles existed. (ii) For an electrostatic field (E-field), define the electrostatic potential (Fi), and explain CONCISELY what is meant by a...

Homework Statement Sketch the space curve represented by the intersection of the surfaces. Then represent the curve by a vector-valued function. Homework Equations Surfaces: z=x2+y2, x+y=0 Parameter: x=t The Attempt at a Solution So, I sketched the space curve represented...

HELP

Homework Statement Is it necessary to have a normal reaction whenever 2 surfaces are in contact with each other? The Attempt at a Solution I thought the answer was "no". But my book says "yes". I can support my answer with an example: the normal force between the surface of a block...

I'm trying to finish reading/understanding the textbook we used in Calculus III (multivariate), as we only covered chapters 12-18, but I'm stuck on something. We used McCallum/Hughes-Hallett/Gleason, and I'm referring to section 19.3 (if you have the text) which is about flux integrals over...

Hi, I need some good amount of information regarding the types of control surfaces being used to control and maneuver the missiles. i couldn't find this stuff on my own. so, please help me. thanks in anticipation Abhishek

Hi, all, I have a question about coloring a 3D parametric surface in Mathematica. Setup: Take as given a surface M in R^3 and a parameterization of that surface p:[a,b] x [c,d] -> R^3. Let f:M -> R be a function defined on M. Question: How can I plot this surface so that points p...

Stereographic Projection for "general" surfaces First off, sorry if this is in the wrong forum. I came across this while studying computer vision, but it's of a somewhat mathematical nature. Please move it if it's in the wrong place. In the book I'm reading*, stereographic projection is used...

hi all, I have read papers in which they specify the dangling bonds on the surfaces and tey saturate it with hydrogen forexample; 1. should it be hydrogen atoms or ghost hydrogen? 2. how to specify the dangling bonds? 3. any suggestion for specifying the position of these hydrogens in...

Homework Statement Let C be the intersection of the two surfaces: S1: x^2 + 4y^2 + z^2 = 6; s2: z = x^2 + 2y; Show that the point (1, -1, -1) is on the curve C and find the tangent line to the curve C at the point (1, -1, -1). Homework Equations partial derivates, maybe the gradient...

[b]1. This problem is part of an engineering model I am working on for a class. I am ultimately trying to model the torque applied to a bottle as a function of the static/kinetic coefficient of friction between it and the rubber cone it is being torqued by (The reason for this being bottle caps...

Homework Statement One wave function of H like atom is \psi=\frac{\sqrt{2}}{81\sqrt{\pi}a_{0}^{3/2}}(6-\frac{r}{a_{0}})\frac{r}{a_{0}}(e^{\frac{-r}{3a_{0}}})cos \theta How many nodal surfaces are there? 1)1 2)2 3)3 4)none of these The Attempt at a Solution Its an objective...

Hi all. This is one of the problems that I was asked to do for my General Relativity class. I know this may look a little long, but if anyone can help me out with ANYTHING about this problem, I will greatly appreciate it. Homework Statement Consider the family of hypersurfaces where each...

Hello, I have a quick question regarding an http://www.sciencenews.org/view/generic/id/38466/title/Blueprint_to_repel_oil_and_water" that I just read on ScienceNews regarding hydrophobic surfaces. In the second to last paragraph it's quoted that "although hydrophobic surfaces readily shed...

Are there surfaces that have a geodesic curve which completely covers the surface, or (if that's not possible) is dense in the surface? In other words, if you were standing on the surface and started walking in a straight line, eventually you would walk over (or arbitrarily close to) every...

I've been doing some experimentation with plotting parametrized surfaces in maple, and I would like to get some ideas for more things I could do. I'm not very clever at figuring out new parametrizations, but I'd like to do some things with seashells. The plots I'm coming up with are very...

Homework Statement For the following system 1) Find the tension in the string 2) find the acceleration of each of the masses The diagram of the system looks like this ...O-----|200g|-----O ...|.\___|____|___/.| __|__....__|__...

In general, say: we have a surface: y^2/4 - x^2/3 - z^2 = 1 I know that this is a hyperboloid of 2 sheets, since the xz trace: x^2/3 + z^2 =-1 doesn't exist, But for the other traces: xy trace: y^2/4 - x^2/3 = 1 and yz trace: y^2/4 - z^2 = 1 Which are both hyperbolas - how do...

Just when I thought I got the hang of tangent planes and surfaces there comes a question I haven't quite seen before z = ln (x^{2}+3y^{2}) Find a normal vector n and the equation of the tangent plane to the surface at the point (2, -1, ln 7) So keeping the cartesian equation in mind: z =...

Suppose that F(x,y) = x^{2}+y^{2}. By using vector geometry, find the Cartesian equation of the tangent plan to the surface z = F(x,y) at the point where (x,y,z) = (1,2,5). Find also a vector n that is normal to the surface at this point...