# Tagged Questions

Surface is a two-dimensional submanifold of three-dimensional Euclidean space.

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### Cylinder with two puncture and one cone point

I have questions about a Cylinder with two puncture and one cone point of order $3$, is it a singular pair of pants or there is other possibility?? This surface is not compact as it has two puncture, ...
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### What is the difference between surface and algebraic curve in general?

The question may seem dumb at first glance. But I couldn't figure out a satisfying answer after some research. A friend of mine told me that in an interview, she was asked to explain the sliding mode ...
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### Questions about surface integrals and an example problem

It is double integral $(x + y) dS$ where $S$ is the part of the cylinder $y^2 + z^2 = 4$ . With $x$ being between $0$ and $5$ First question, if we want to get the integral of the surface of a ...
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### Volume and surfaces

i need help. Be : $X =(x,y,z)$ and $$T=\{x\in R^3\mid X=\begin{bmatrix}(1+rsin(u))cos(v)\\(1+rsin(u))sin(v)\\rcos(v)\end{bmatrix} ,\\0.5\geq r \geq 0,\\ 2\pi\geq u \geq 0 \\ 2 \pi\geq v \geq0$$ ...
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### Is there a simple way to decide if a hyperboloid is one-sheeted or two-sheeted, given the quadric equation?

Let us say that we have a quadric equation, whose solution set lies in $\mathbb{R}^3$, and you know it's a hyperboloid. Is there a way to analytically decide through a criterion if the hyperboloid is ...
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### Is this spiral known?

Parametrized as $$\sec \theta \,( p \cos(\theta+ \alpha), \,p \sin(\theta+ \alpha) , c\alpha),$$ the spiral is plotted $(-\pi/4<\theta< \pi/4;\,\,0< \alpha < 3 \pi)$ for $p= 1$ ...
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### Existence of closed level sets on a surface for some field

Consider an infinite 3D space with only 2 things in it: wind and a solid object. Wind evidently blows around this solid object over its rigid surface. Bascially we are trying to set up a pure field. ...
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### Normal to surface at point

I have this function: $F(x,y,z)=x^2−y^2−z^2+4$ where $z\ge 0,0\le x \le 2,0 \le y \le 2$. How can I find the normal at some point $P=(p_x,p_y,p_z)$? I have tried to calculate the derivatives of ...
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### surface of the saddle [closed]

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
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### Absolute value of an RBF distance is less than the absolute value of an actual distance

I have a radial basis function with a linear kernel f(r)=r in 3D. I constructed the surface based on this RBF and noticed that the absolute value of actual distance from any point to the constructed ...
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### Surface Area of Stainless steel scoop

I want to calculate surface area of Stainless steel Scoop. I am trying different circle and cylindrical formula but not succeeded. please help me out
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### How to calculate a surface area of a river?

I am doing a math exploration and I was wondering if someone could help with this problem. What will I need to use in order to calculate SA of a river? What parts of math are used? What info will I ...
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### Find surface area that lies above a triangle

Determine the area of the part of the surface $z=2 + 7x + 3y^2$ that lies above the triangle with vertices $(0,0)$, $(0,8)$, and $(14,8)$. I do not know what formula to use to attempt this problem!
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### How to determine the equation of shortest path on any 3d surface between two given points?

I am working on draping of woven composite and I have to determine the equation of shortest path on 3D surface (i.e. $z=x^2+y^2$) between two given points in order to get the yarn path between two ...
The parametric equation $x=a\cos(bt)\cos(t)$, $y=a\cos(bt)\sin(t)$ where $a$ & $b$ are constants and $t$ is parameter gives a rose curve which looks like, On a similar basis, is there a equation ...