Tagged Questions
0
votes
1answer
60 views
Stereographic projection of ellipsoid
I am really new in geometry and especially in working with stereographic projection, so excuse me, please, if my question is too easy.
Given is the ellipsoid: $E = \left \{ (x,y,z)\in \mathbb{R}^{3}: ...
3
votes
0answers
56 views
Curvature on topological spaces
On what subsets of the category of topological spaces are different notions of curvature defined?
1
vote
0answers
55 views
Generate coordinates for abstract triangulation
I have an abstract triangulation, which consists of nodes without coordinates and connectivity information (the triangles themselves). I also know that each link has a fixed length. For simplicity we ...
3
votes
2answers
129 views
line equidistant from two sets in the plane
Suppose $A$ and $B$ are disjoint subsets of the plane, both closed, nonempty, and connected. Define $E(A, B)$ as the set of points in the plane equidistant from $A$ and $B$. For example, if $A$ is a ...
1
vote
1answer
70 views
Given lattice G; parameters of torus R^2/G?
This should be a simple, known result, but I can't seem to find it.
Given a lattice $\Gamma = m\mathbb{Z} \times n\mathbb{Z}$, $\mathbb{R}^2/\Gamma$ is topologically a torus. For suitable $m$ and ...
9
votes
1answer
214 views
Covering points on a sphere with a disk
Suppose $m$ points ("sites") are selected on the unit sphere $S^2$. For a given radius $r < \pi$, we can define a disk around any point on the sphere as the set of points at geodesic distance at ...
5
votes
0answers
202 views
Points in the plane at integer distances
Does there exist a set of $n$ points $p_1,p_2,...,p_n$ in the plane, all at mutual integer distances to each other, and an $e>0$, such that the following statement holds:
For all $a,b$ with ...
3
votes
1answer
113 views
Planar kelvin problem
What is the minimal possible value of the maximal total sidelength shared by any two tiles in a tiling of the plane if all tiles have the same area A?
total sidelength = Length-integral of the curve ...
7
votes
2answers
111 views
$n$ points on every line
For which integers $n$ is it possible to find a subset $S$ of $\mathbb R^2$ such that every infinite line contains exactly $n$ points of $S$?
