All Questions
109 questions
0
votes
1
answer
229
views
Is this bounded?
May be better to ask for help here. Let $v_{1}$, $v_{2}$, $\ldots$, $v_{m}$ be the vertices of a
convex polygon in the plane and $v_{m+1}$ be a vertex in the interior
of the convex polygon. Connect ...
- 1
5
votes
4
answers
1k
views
Coloring Points in the Plane
Suppose one wants to color the points in the plane so any two points at distance one apart are different colors. How many colors are needed?
I heard this problem when I was a kid. Back then the most ...
- 14k
7
votes
3
answers
866
views
Not quite regular polyhedra
Take a naive interpretation of regular polyhedra:
All vertices (including epsilon ball) congruent
All edges congruent
All faces congruent
We can now find interesting families by removing one ...
- 3,532
4
votes
0
answers
443
views
Intersection of pencils in $\mathcal{R}^2$
Consider $9n$ pencils through non-collinear points $p_1, \ldots , p_{9n}$ in $R^2$ each consisting of at most $n$ concurrent lines. Define the intersection $S$ of these pencils to be the set of points ...
- 85.6k
2
votes
1
answer
370
views
Large subgroups of the Hamming cube
Let's consider the abelian group $\mathbb{Z}^N_2$ equipped with the Hamming metric (the hypercube).
Suppose I have a subgroup of this hypercube (not necessarily a subcube) which is generated by a set ...
- 6,342
8
votes
0
answers
358
views
Coloring toroidal polyhedra with convex faces?
Consider a toroidal polyhedron, which is a topological torus, in which all faces are planar, two faces meet in at most an edge, and adjacent faces are not coplanar. The Szilassi polyhedron has 7 non-...
15
votes
3
answers
1k
views
Representation of vectors in $\mathbb{R}^2$ via differences of small vectors.
Is the following fact true?
Let $v_1,\ldots, v_k \in \mathbb{R}^2$, $\|v_i\|\leq 1$, be vectors that add up to zero. Does there exist a permutation $\sigma\in S_k$ and vectors $w_1,\ldots, w_k \...
- 43.2k
5
votes
2
answers
523
views
Maximal area coverable by $k$ disjoint isosceles triangles contained in a triangle of area 1.
Given a triangle $\Delta$ of unit area, how much area can always be covered by $k$ isosceles triangles contained in $\Delta$ and intersecting at most at their boundaries?
The answer is easy for $k=1$....
- 6,523
2
votes
1
answer
247
views
Are combinatorial configurations whose Levi graphs may be represented as covering graphs over voltage graphs realizable with pseudolines?
This question is related to this previous question. Many combinatorial configurations have Levi graphs which may be represented as derived graphs obtained from voltage graphs over a cyclic group; in a ...
CommunityBot
- 1