surface Definition and Topics - 21 Discussions

A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is the portion with which other materials first interact. The surface of an object is more than "a mere geometric solid", but is "filled with, spread over by, or suffused with perceivable qualities such as color and warmth".The concept of surface has been abstracted and formalized in mathematics, specifically in geometry. Depending on the properties on which the emphasis is given, there are several non equivalent such formalizations, that are all called surface, sometimes with some qualifier, such as algebraic surface, smooth surface or fractal surface.
The concept of surface and its mathematical abstraction are both widely used in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface. The concept also raises certain philosophical questions—for example, how thick is the layer of atoms or molecules that can be considered part of the surface of an object (i.e., where does the "surface" end and the "interior" begin), and do objects really have a surface at all if, at the subatomic level, they never actually come in contact with other objects.

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  1. pairofstrings

    B Boundary or Surface?

    Equation of circle: ##x ^2+y ^2=1##. Is this equation describing boundary or a surface? Thanks.
  2. T

    A Identifying a surface as a cone

    Hi, I’m using some CAD software trying to automate some surface identification, and I’m looking to find a way to identify whether a surface is a cone. I will have access to vertices and normals at discrete points on the surface, but it will be expected that the number of these points will be...
  3. QuarkDecay

    Flow (liquid or gas) across a rotating surface's face

    << Mentor Note -- Two threads on the same question merged into one thread >> How does the maximum Power equation change if there's an angle to the way the wind falls into the wind turbine's blades? Example, when it falls vertically to the blades, it's Pmax= 8/27Sρu13 But if there's for...
  4. CollinsArg

    I Surface area of a revolution, why is this wrong?

    Why is this way of thinking wrong?. can't I assume that when Δx tends to zero is a sufficient approximation of what I want to get? It confuses me with the basic idea of integrating a function to get the area beneath a curve of a function (which isn't also as perfect) . PD: I put Δx tends to...
  5. AllenFaust

    Hamiltonian for a dimer approaching a surface

    Hi! it's been a day since I have started this problem. I was wondering how I could arrive to this Hamiltonian? And I'm a bit at a lost on how exactly to derive this? I hope anyone can help me with this, even a suggestion of good starting point would be much appreciated. Basically the problem...
  6. R

    Is there any way to calculate this integral?

    I have done it by the parametric form of σ, but if I change σ to implicit form that is G(x,y,z)=x^2+y*2+z^2-R^2=0 I don't know how continue. The theory is: where Rxy is the projection of σ in plane xy so it's the circumference x^2+y^2=R^2
  7. W

    Thermal resistance without area

    I'm (self)studying the physics of heat transfer at the moment. My book gives a relationship between heat transfer rate and thermal resistance as ##\phi=\frac {A \Delta T} {R}##. My book is not in English, so hopefully that is not the cause of this misunderstanding. I double checked that heat...
  8. Zaent

    I Mean and Gaussian curvature for a Gaussian 'hill' seem wrong

    I'm hoping someone can help check whether my final contour plots look plausible based on the surface. I haven't done too much differential geometry but I've needed to work with Gaussian/Mean curvature for a simple 3D gaussian surface. Here's an example: (A = 7, a=b=1/(3.5)^2) It's...
  9. U

    B Integrating to find surface area/volume of hemisphere

    To find the surface area of a hemisphere of radius ##R##, we can do so by summing up rings of height ##Rd\theta## (arc length) and radius ##r=Rcos(\theta)##. So the surface area is then ##S=\int_0^{\frac{\pi}{2}}2\pi (Rcos(\theta))Rd\theta=2\pi R^2\int_0^{\frac{\pi}{2}}cos(\theta)d\theta=2\pi...
  10. S

    How to parameterize these surfaces?

    Homework Statement Calculate ##\iint { y+{ z }^{ 2 }ds } ## where the surface is the upper part of a hemisphere with radius a centered at the origin with ##x\ge 0## Homework Equations Parameterizations: ##\sigma =\left< asin\phi cos\theta ,asin\phi sin\theta ,acos\phi \right> ,0\le \phi \le...
  11. lila12345

    I Surface of revolution of a donuts

    HELP I can't find the surface of revolution!! By donuts I mean a circle that doesn't touch the axes (tore in french) y^2+(x-4)^2=2^2 is my function ( y^2+x^2=r^2) and the axe of rotation is y so y= sqrt(r^2-x^2) the formula I know : 2* pi (Integral from a to b (F(x)*sqrt( 1+ (f``(x))^2))...
  12. tommyxu3

    I Make a Pseudo-Riemannian Metric Conformal

    Hello everyone: I studied in differential geometry recently and have seen a statement with its proof: Suppose there is a Riemannian metric: ##dl^2=Edx^2+Fdxdy+Gdy^2,## with ##E, F, G## are real-valued analytic functions of the real variables ##x,y.## Then there exist new local coordinates...
  13. T

    A Predicting Fermi Surface from Chemical Formula

    Hi, I was hoping I could get some things cleared up. Recently my Solid State professor mentioned that we could simply, from the chemical formula, predict where the band crossings are going to be. For example, take LaFeAsO. Since La has a valency of +3, Fe of +3, As of -3, and O of -2, he...
  14. N

    I If radiowaves are reflected from objects (i.e planets)...

    ...and they can penetrate a bit in the surface, we could image the subsurface right? I do not see the problem... Help please!
  15. S

    Energy loss when boiling in an water experiment -- help please

    Homework Statement Hi, as a part of my lab report I have to conduct this experiment : Fill a pot with tap water and boil it, determine then how much of the energy that the kitchen surface produced, actually went to the water itself. Consider the water having an initial temperature of 10 °C. In...
  16. T

    Reference wanted: surface and interface

    I am a Ph.D. student just beginning my research. Recently, I found several papers about surface and interface interesting, so I want to know more about this area. However, I cannot find any specific review which can give me an overview of this area. Can anyone give me a link to such literature?
  17. norlesh

    Surface treating mild steel for hard vacuum

    I understand mild steel is very bad at out gassing so is never usually considered for hard vacuum applications. But if the decision was constrained by other factors would it be possible to apply a surface treatment or coating to the internal walls of the vessel - am I correct in assuming that as...
  18. G

    Determining the brightness on a projected surface

    I'm trying to determine how bright my projection image will be on a projected surface. I'm struggling to find a formula for this. I'm using (for example) the Canon Rialis projector which is 4500 lumens. I would be using the zoom lens with maximum zoom so the throw ratio would be 7:1. At a...
  19. E

    Finding point on paraboloid surface given normal line point

    Homework Statement [/B] Find the coordinates of the point P on the surface of the paraboloid z=6x2+6y2-(35/6) where the normal line to the surface passes through the point (25/6, (25√22)/6, -4). Note that a graphing calculator may be used to solve the resulting cubic equation. Homework...
  20. J

    Aluminum structure modifications for use near a very hot fire

    I'm building an frame out of solid 5/8 inch thick aluminum square bars. this frame will be around a fire temps close to melting points but there will be insulation in make sure it won't melt. I was thinking about drilling holes in the free space of the aluminum to reduce it's weight and if you...
  21. S

    Suggesions on tablets for use in physics classroom

    The school in which I teach is going to pilot a tablet for each student in a class next year. My physics class is going to be part of this pilot. Currently they are looking at ipad/surface/chromebook. Does anyone have input good or bad on any of these for use in class as well as with labs...
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