In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solids; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.
Topological surfaces are sometimes equipped with additional information, such as a Riemannian metric or a complex structure, that connects them to other disciplines within mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical world.
Does anybody know any neat measurements one can do to characterise a surface? I'm thinking generally of rough surfaces such as the ones you come across in epitaxial systems.
In other words:
If I have two ensembles of surfaces, what is the best method to use to determine whether the same...
Hey just need a quick clarification here.
I am reading conflicting arguments. One argument states that to find the nodal surfaces of an orbital you take the result of n-1 the other argument states that the number of nodal surfaces of an orbital is equal to n.
Can someone please clear this...
[SOLVED] Parametric Surfaces and Their Areas
Hello,
I am having problems visualizing a concept. First I will post my question as it is given in Jame's Stewart's Fourth Edition Multivariable Calculus text, Chapter 17, section 6, question 17.
Find a parametric representation for the given...
black surfaces apparently absorbs all light, that's why it appears black, but does it ever reflect light off its surface?
what if its a polished black suface..we could actually see our own reflection on these surfaces.. so is there light being reflected at all? is there any difference from the...
A positive test charge is placed at the center of a spherical Gaussian surface. What happens to the net flux through the Gaussian surface when the surface is replaced by a cube of the same volume whose center is at the same point? or When the sphere is replaced by a cube of one third the volume...
I have a new question:
"In applying Gauss's Law describe the types(s) of charge distribution for which (a) a spherical gaussian surface is useful and (b) a cylindrical gaussian surface is useful"
please help!
I'm wondering if it is true that any surface can be equated to a weighted sum of a basis of surfaces differring only by genus? I think this is asking whether the path integral formulation for strings is more general.
Thanks.
I am in a materials science class and need to come up with a course project. One thing that interested me was in an article that I read in the paper a while back. It was about the development of some kind of coating that could be applied to surface that could render it permanently sterile. I...
I am trying to learn a little bit more about geometry of surfaces and some differential geometry concepts like principal, gaussian an mean curvatures.
I have found some interesting material at mathworld.wolfram.com but as usual there is a quantity of little incorrect details.
Is anybody...