Surfaces Definition and 425 Threads

I was lying awake the other night and thinking about Pi and flatlanders. I haven't done a lot of topology reading, so forgive my naivete. Pi on a flat surface is a number we know well, but what happens to the ratio of a circle's diameter to its circumference on curved surfaces? First question...

Homework Statement Problem 18B.13 from Transport Phenomena, BSL. Tarnishing of metal surfaces. In the oxidation of most metals the volume of oxide produced is greater than that of the metal consumed. This oxide thus tends to form a compact film, effectively insulating the oxygen and metal from...

Problem: Consider two parallel and large sheets with a surface area . One has a charge and the other is uncharged. q | | | | | | | | | | What would be the electric fields on the three regions as divided by the sheets ? General solution to problems like as told...

Homework Statement Find the volume of the solid bounded by z=x^2+y^2 and z=8-x^2-y^2 Homework Equations use double integral dydx the textbook divided the volume into 4 parts, The Attempt at a Solution [/B] f(x)= 8-x^2-y^2-(x^2+y^2)= 4-x^2-y^2 i use wolfram and got 8 pi, the correct...

Homework Statement [/B] Mass m starts sliding down on a rough surface with coefficient of friction μ. it reaches point B and starts sliding frictionlessly till it reaches point D without velocity, i.e. without escaping the arc. What is the maximum length AB=x0 not to escape the arc. What is...

Homework Statement set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations y = 4 - x^2 z= 4 - x^2 first octant The Attempt at a Solution I am fairly confident in my ability to evaluate double integrals , but I am having a problem figuring...

Homework Statement Compute the volume of the solid bounded by the four surfaces x+z=1,x+z=−1,z=1−y2,z=y2−1 Homework Equations Fubini's theorem? The Attempt at a Solution I have tried to visualize this solid and define the limits; when I attempted to integrate by dxdzdy (in that order), I set...

I've read that tides deform the Earth's crust by about 40cm. When I try to visualize the tidal bulge approaching me and then receding away from me, it seems like the local surface under my feet would tilt slightly one way as the bulge approaches, then level out, and then tilt slightly the other...

Homework Statement Homework Equations The Attempt at a Solution so to start this off, I choose a random point, by setting u and v = 0 giving me the point (0,3,1) but I have no idea how what to do next. how do I find ua and vb?

Homework Statement A non-conducting sphere (radius 11.3 cm) has uniform charge density ρ = 0.596 μC/m3. Find the distance, in meters, between equipotential surfaces V1 = 16.2 Volts and V2 = 42.3 volts. (Distance is always positive.) Homework Equations V=kq/r ρ=Q/V The Attempt at a Solution...

Hi all Making this title was harder than I thought. It certainly makes the topic look more advanced than it actually is. I studied differential geometry during my masters but never went much in depth, just enough so I could apply basic concepts to my specific problems at the time. Now I'm...

This the breaktrhough by bousso, which was a student from Hawking. It sees it was accepted under peer review magazines in 2 months. You can find the versions at: 1. arXiv:1504.07660 [pdf, other] Proof of a New Area Law in General Relativity Raphael Bousso, Netta Engelhardt Comments: 15 pages...

Homework Statement Parameterize the curve of intersection of the two surfaces: x^2+y^2+z^2=14 z=y^2-x^2 Homework EquationsThe Attempt at a Solution I tried manipulating the equations above but can't seem to get a nice parameterization which I can use to do the rest of the (calculus) problem.

Homework Statement Find the volume of the solid bounded by the surfaces ## (x^2 + y^2 + y)^2 = x^2 + y^2 ## ##x + y + z = 3 ## and ##z = 0## Homework EquationsThe Attempt at a Solution I begin by converting to polar coordinates to do a cylindrical integration with 3 variables. ## (x^2 + y^2 +...

Hi, Just to let you know my level of knowledge/ability, I studied a degree that included some dynamics, but that was nearly 15 years ago, so I'm rusty. I'm a games programmer, and I tend to understand code (or things that can be translated into code) more easily than hardcore maths equations...

I have been working on designing something in SolidWorks for the first time, which involves several parts with surfaces that slide into one another. I am wondering if there is a table or a standardization in terms of the distance that should be left between metal surfaces with sliding parts. I...

Hi, There is a result that if two manifolds ## M_1, M_2 ## ( I don't know to what extent this generalizes to other topological spaces) intersect transversally, say in ##\mathbb R^m ## , then the dimension of the intersecting set is given by m - ##\Sigma Cod(M_i ) ; i=1,2##, where ##Cod(M_i):=...

Hello, I am studying for an analytic geometry final but I am totally lost for this problem... We didn't even cover this topic in class (my prof didn't show up for class for two weeks) and I have no clue on how to do it. If anyone could help I would appreciate it. Question: Prove that the...

With laser pointers being so ubiquitous, everyone is familiar with the sight of interference patterns on paper, ground glass and other surfaces (not to mention more subtle experiments like this one): Quantum Eraser -- which has been discussed recently in other threads. We take it for granted...

Hello everyone, thank you for helping me in the other post, this one is different but includes pressure and how to calculate how much of it is present when an object is being "indented" or dug into. I come from a forum that discusses fictional characters a lot and we find it highly enjoyable to...

Homework Statement Purcell 2.10 [/B][not the problem I'm asking about, but needed for Purcell 2.11 which I am asking about] A thin rod extends along the z axis from z = -d to z = d. The rod carries a charge uniformly distributed along its length with linear charge density \lambda. By...

Homework Statement I am looking to find the parametrization of the curve found by the intersection of two surfaces. The surfaces are defined by the following equations: z=x^2-y^2 and z=x^2+xy-1 Homework EquationsThe Attempt at a Solution I can't seem to separate the variables well...

The atoms in a metal (ex. Cu) are arranged as a 3-D grating. But to our common sense ,smooth metal surfaces only reflect lights. Why can't we see diffraction from metal surfaces?

Homework Statement Homework EquationsThe Attempt at a Solution I could know the pressure in point B If I calculate the heigh of pressure I got: But I don't know where is my free surface in the container 3, is it down?? I don't know how to keep doing it...

Hey! :o Draw or describe the level surface and an intersection of the graph for the function $$f: \mathbb{R}^3 \rightarrow \mathbb{R}, (x, y, z) \rightarrow x^2+y^2$$ I have done the following: The level surfaces are defined by $$\{(x, y, z) \mid x^2+y^2=c\}$$ - For $c=0$ we have that...

Hey! :o I am looking at an exercise that asks to describe the surfaces r=constant, θ=constant and z=constant in the cylindrical coordinate system. The cylindrical coordinates are $(r, \theta , z)$, that are defined by $x=r \cos \theta , y=r \sin \theta , z=z$ $r=\sqrt{x^2+y^2}, z=z ...

Homework Statement I know that the equation ##z = f(x,y)## gives a surface while ##w = f(x, y, z) ## gives an object that has the same surface shape on top as ##z = f(x,y)## but also includes everything below it. If these statements are correct, what is the level surface of a function of three...

Homework Statement Given the eqn x=2, y=sin(t), z=cos(t), draw this function in 3-space. Homework Equations ABOVE^ The Attempt at a Solution I did this: x^2+y^2+z^2=2^2+(sin(t))^2+(cos(t))^2=5 Therefore we get x^2+y^2+z^2=5 Which is the eqn of a sphere with radius root5. My friend said it's...

Homework Statement Sketch a picture of the cone x = sqrt(y^2+z^2) , and elliptic paraboloid x = 2−y^2−z^2 on the same grid. Although the picture does not have to be perfect, indicate clearly the orientation of both figures relative to coordinate axes. Identify the curve at the intersection of...

Homework Statement I have uploaded a file that shows the question.[/B]Homework Equations I believe the only relevant equation is: flux = Q(enclosed)/E(knot)[/B]The Attempt at a Solution Well I have some questions first. The problem statement says that the sphere on the left has a net...

Homework Statement Two charged, parallel, flat conducting surfaces are spaced d = 1.3 cm apart and produce a potential difference ΔV = 625 V between them. An electron is projected from one surface directly toward the second. What is the initial speed of the electron if its comes to rest just at...

Hi Folks, 1) Can anyone provide some online sources on how to parameterize quadric surfaces of order 2 as shown in this link Algebraic Surface -- from Wolfram MathWorld Is there a standard technique? I did a google search with no useful info. Thanks

In other words, when we take for potential function instead of F the square root of (6F/6x)²+(6F/6y)² (in the particular case of two-dimensions). Does this lead to anything interesting?

Theory and my Understanding: So I understand how the frank condon principle let's us effect electronic transitions instantaneously, since the motion of nuclei (on the timescale of such electronic transitions) is quite slow. Consequently, when a photon of light is absorbed you can have an...

I'm puzzled by a phenomenon that my daughter pointed out to me. If you have no plastic ware in the dishwasher, your glass and ceramic dishes will dry faster. Slow evaporation from plastic is easy to understand; the water beads up and presents a smaller surface area. What I'm not clear on is why...

I am looking for a introductiory book on Riemann surfaces in context of bosonic String theory, or heterotic String theory for that matter. Prices should be affordable but should not matter, of I nead guide books this also does not matter...Help is seriusly apreciated.

Hi, let ## \alpha, \gamma ## be non-isotopic curves in a compact, oriented surface S. There is a result to the effect that ## S-\alpha## is homeo. to ## S- \gamma ## . This is not true as stated; we can , e.g., remove a disk (trivial class) in a copy of S and then remove a meridian ( a...

Homework Statement http://postimg.org/image/4fhu5k9r9/ Can someone explain what is meant by 'missing water' in this solution diagram The original question diagram had no such water above the gate AB Homework Equations The Attempt at a Solution

When looking through a triangular prism, I found that a black shape on a white back ground causes the blue end of the spectrum to be on the top of the black shape, and the red/yellow end is directed towards the bottom. The reverse is true for a white shape on a black background. Why is this?

I have attached an image... Okay, so I have been stuck on this problem for like 2 hours now and I have no idea how to find r(x). I know the trace is the intersection of the plane and the surface. My first attempt was to substitute the plane y+2x=0 equation for the surface equation by solving...

ok so this is the part I am really struggling with. we need to be able to recognize an ellipsoid, cone, elliptic paraboloid, hyprboloid of one sheet, hyperbolic paraboloid, hyperboloid of two sheets given an equation. he's going to give us an equation of one and ask us to identify and sketch the...

How does the texture of a surface affect the concentration of charge on that surface? Say we compare a balloon (smooth) and a football (textured) (ignoring material differences) and give them the same total charge. Then we introduce dust particles. How do the two surfaces attract dust...

I'm looking for a book or two that details affine spaces and transformations, then differential geometry of surfaces in affine spaces, starting at a level suitable for a year 1-2 undergraduate. In particular, I'd like to understand a few properties (e.g. what's the gradient and curvature at a...

why is the electric field zero , if the closed gaussian surface doesn't enclose any charges. but,, if the charges are present at a distance outside the conductor?? and why isn't the electric field zero inside the gaussian surface, if there are charges distributed on the surface of the...

Hello , please help me out , I can find the E field of a sphere on google and read that there is no field on the inside of the sphere , but what is the e field of a torus ? Not on the inside but on the outside surfaces also in the inner loop or the middle ?

Question : The top of the atmosphere is at about 400 kV with respect to the surface of the Earth, corresponding to an electric field that decreases with altitude. Near the surface of the Earth, the field is about 100 V/m. Why then we do not get electric shock as we step outside our house into...

Homework Statement You measure a uniform electric field of 13.3 x 10^3 N/C between two equipotential surfaces. One surface is at a potential of 1543 V and the other is at 951 V. What is the separation between the two surfaces? Homework Equations Eave = - deltaV/delta x The Attempt at...

Why do things like grease, cheese, butter, jam, etc. stick to smooth surfaces like a butter knife or teflon? What are the ways in which they would not stick and be allowed to release without being heated?

Homework Statement Drawing surface ##f(x,y) = ...## or ##r(t) = <f(t),g(t)>## etc. The Attempt at a Solution I've been working on drawing space curves lately, by breaking into separate planes and by level curves. I'm struggling w/ this topic. (1) If I'm not mistaken, this is fundamental in...

Homework Statement (a) Show that the four points r1 = (1, 0, 1), r2 = (4, 3, 5), r3 = (6, 4, 6) and r4 = (3, 1, 2) are coplanar and the vertices of a parallelogram. Let S be the closed planar region given by the interior and boundary of this parallelogram. An arbitrary point of S can be...