Linked Questions
10 questions linked to/from Distributing points evenly on a sphere
13
votes
5
answers
1k
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Packing obtuse vectors in $\mathbb{R}^d$
I came across this attractive theorem:
Theorem. In $\mathbb{R}^d$, there can be at most $d+1$ vectors that
form an obtuse angle with one another.
This was proved1 as a corollary of a lemma about ...
- 151k
18
votes
3
answers
627
views
Construction of an optimal electron cage
I will describe the question first in 2D, but my interest is in $\mathbb{R}^3$.
An electron $x$ will shoot from the origin along an initial vector $v$. You know the speed $|v|$ but not the direction.
...
- 151k
7
votes
1
answer
389
views
Packing disks of infinitesimal diameter on a sphere: the asymptotics of the Tammes problem
This is an elaboration on MO Question 212550: given $ 0 < 2a << 1 $, how many points can be placed on the unit sphere, subject to the constraint that any two of these points must be at ...
- 347
1
vote
2
answers
334
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How to calculate all rays inside a sphere which are all equally angled from eachother
I am creating a 3D computer simulation and I want to build a sphere from rays coming from the center of the sphere. Imagine a sphere consisting of all dots/particles at the end of the rays.
The dots ...
- 113
2
votes
1
answer
292
views
Facility location on manifolds
Facility location studies optimal placement of a certain number $n$ of points (facilities) in some region $R$. (https://en.wikipedia.org/wiki/Facility_location_problem)
The minimax facility location ...
- 5,979
4
votes
1
answer
220
views
The link and equivalence between variant definition of computation model and computational complexity over reals
To unify the numerical computation and classic computability theory, or to pave a foundation for the numerical computation, mathematicians present variant computation model and computational ...
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11
votes
0
answers
216
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Electrons on a pancake ellipsoid
The problems of minimizing the potential energy of electrons
on a sphere, or maximizing the smallest distance between the electrons,
have been well-studied.
E.g., see the
earlier MO question
"...
- 151k
3
votes
1
answer
109
views
The angle of two closest points among $N$ points evenly placed on the $d$-dimensional unit sphere
Some previous questions (here and here) ask for algorithms to place $N$ points evenly on the $d$-dimensional unit sphere. In my case, what I am looking for is that, given these $N$ points that are ...
- 139
6
votes
0
answers
164
views
Sets of points avoiding small angles
(1) $\mathbb{R}^2$.
I'd like to place $n$ points in the plane so that the smallest angle they
determine is as large as possible.
In a sense, such a point set is in very general position, not only
...
- 151k
1
vote
0
answers
68
views
Facility location and traveling salesman
This question is based on Distributing points evenly on a sphere and Facility location on manifolds
The 'dispersal problem' (which can be mapped to packing disks in many cases) places $n$ points in a ...
- 5,979