Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [surfaces]

For questions about two-dimensional manifolds.

Formally, a surface is a two-dimensional topological manifold. Some examples of surfaces are the plane, the cylinder, the sphere, and the graph of a real-valued function of two variables.

More generally, the term "hypersurface" can be used to denote an $(n-1)$-dimensional submanifold of an $n$-dimensional manifold.

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Is every continous function in $\mathbb{R}^3$ a surface?

there is a knot in my brain. Assume some Datapoints in $\mathbb{R}^3$. I want to fit a surface through them. I found a lot of surfaces such as multiple quadric surfaces (so dont worry that i haven't googled it). I have the following questions: Is…
horsti
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Cut partially a fundamental polygon is valid?

We know that cut/glue are operations in fundamental polygons in order to obtain surfaces. Now, I wonder if you cut partially the fundamental polygon of a torus, with label word $aba^{-1}b^{-1}$, square since one of his vertex until (aproximately)…
user183002
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Determine surface deformation given slight changes in angle of orthogonal vectors

I have a flat, rectangular surface with an evenly-spaced grid. Let's say it is $100 \times 100$ units (in the $X$ and $Y$ directions, defining the coordinates of each grid cell), and $Z = 0$ everywhere. I have placed $10$ randomly-located normal…
Eric Krantz
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Parametrization of a surface 4

So i have this surface, lets say $S$: $$(x^2+y^2+z^2)^3=(x^2-y^2)^2, |x|\leq y$$ So i have to change this into a parametric expression. So, the left side seems something simmilar to a sphere, so i am thinking about using spherical coordinates, but i…
MathIsTheWayOfLife
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What is an open surface bounded by a closed contour

Can someone tell me what an open surface bounded by a closed contour is please? I have difficulties to imagine something.
OcK
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Surface Area of Solid

The figure shows (Can't show the picture because I don't have) A solid consisting of a pyramid of a height $28\mathrm{cm}$ fastened to a cuboid of height $40\mathrm{cm}$ and a square base of sides $30\mathrm{cm}$ each. Find the total surface area of…
A Cool Guy
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Help with appropriate parametrisation

Let $S$ be the surface $x^2+2y^2+z^2=1$. Find a parameterisation of $S$ and use it to find the equation of the tangent plane to $S$ at the point $\left(\frac1{\sqrt2},\frac12,0\right)$. I can't work out an equation of tangent plane using…
Hii
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How exactly do vectors, normals and faces relate in surfaces?

How exactly do vectors, normals and faces relate in surfaces? I understand that given a curve one can construct some kind of surface by duplicating the curve at evenly spaced values of rotation. However, I've also read that these are not enough for…
mavavilj
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How do I find an equation for a boundary between a specific surface and a plane?

I have a surface which is defined by equation $$V = \frac{\frac{C}{D}}{\sqrt{\left(1-\frac{a}{k b}\frac{1-a^{-2}}{b^{-2}-1}\right) \left(1-\frac{a}{k b}\frac{b^{-2}-a^{-2}}{b^{-2}-1}\right)}}$$ Where everything else is a constant except $a, b, V$.…
Dago
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surface of the form $z(x,y)=a xy+b x+c y+d$ through four given points

I know, that for any four points, $(x_0,y_0,z_{00})$, $(x_1,y_0,z_{10})$, $(x_0,y_1,z_{01})$ and $(x_1,y_1,z_{11})$, if $x_0\ne x_1$ and $y_0\ne y_1$, there is a unique surface of the form $z(x,y)=a xy+b x+c y+d$ passing through these points. Can…
Ferenc Beleznay
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surface of the saddle

i need Help. Determine the surface of the saddle $$S={(x,y,z)∈R^3; x^2+y^2<=2, z=x^2 -y^2}$$ and the flow of $v(x) = x$ , by S plane polar coordinates, dx dy = r dr dφ, are helpful. Thanx
Jameel Komaira
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Formula to find lenght of material I need to make a sprint

could somebody write me if you know how to calculate the lenght of a material i need to make a certain spring. I need any true formula you have.
Titi Kokov
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Finding all points on a surface where the tangent plane is parallel to the plane 5x+3y-z=0

Consider z=f(x,y)=x^3 + 2xy + y Find all points on the surface where the tangnent plane is parallel to the plane 5x+3y-z=0 So I took the gradient of f (x,y,z) and got (2x^2 i , 2x+1 j , -1 k) And this vector must be colinear to (5, 3, -1) So (2x^2 …
Jacob
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Giving parametrization of Hyperboloid

I'd like to give a parametrization of an two sheet hyperboloid, such that this parametrization covers both sheets (Without using $±$ symbols). Does that parametrization exist?
LeviathanTheEsper
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How to mathematically formulate the surface of a spring?

I would like to mathematically map the surface of a cylinder constructed like a coil pot (or compressed spring), where the surface area and height of the pot is a function of the length of the coil, and the length of the coil is a function of time.…
Christina I.D.
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