All Questions
8
questions with no upvoted or accepted answers
16
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0
answers
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Properties of the projection onto a nonconvex set
Consider a set $\Omega\subseteq\mathbb{R}^n$ being "sufficiently regular", for example being the image of a $C^1$ mapping from $\mathbb{R}^p$ for some $p\ge1$. We may then consider the mapping
$$
g:\...
- 3,146
6
votes
0
answers
141
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Do balls optimize the boundary area for a fixed volume?
I recently saw this question, asking if the circle is the planar figure which has the least perimeter given the area. As far as I know, this is a classical problem, and the answer is affirmative. I am ...
- 12.7k
4
votes
0
answers
63
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closed curve mapping problem
I have this interesting, seemingly difficult problem I came across while think about rendering. It seems simple enough that I suspect it might have a name already (and hopefully be solved), but I can'...
- 93
2
votes
0
answers
54
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Identify a point in the disc that is as far away from each point of S as possible Ask Question
I have a question.The question is this.
Say you have a finite set S of n points in a circular disc. Think of the points in S as houses on a circular island. You want to locate a garbage incineration ...
- 121
0
votes
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60
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Where will a plane intersecting a cone maximize the distance to inscribed spheres? (V. Arnold)
A cone is cut by a plane, making a closed curve. Two spheres, each inscribed into the cone, are tangent to the plane, at points $A$ and $B$ respectively.
Find the point $C$ on the cut line (i.e. the ...
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0
votes
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answers
97
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What is the connection between optimization and symmetry?
I have found that in many optimization problems, there is some sort of "local symmetry" phenomena going on. For example, suppose we have a 'nice' function which has $f'(x)=0$, then we will ...
0
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How would you go about proving that the right cone is the most optimal pyramid
Im trying to figure this out. Like you could go one by one optimizing a square pyramid by minimizing its surface area for a given volume. Eventually when you get up to an decagon based right pyramid, ...
- 141
0
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145
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How to compute the geometric center of a curved manifold defined by a set of point?
Suppose that I have a set of points E which belong to a manifold. Typically a surface mesh like that.
$$E=\{x_{0},x_1,...,x_n\}$$ where the $x_i$ are the points coordinates in 3D such that : $x_i = (...
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