All Questions
5 questions
18
votes
1
answer
1k
views
Sperner's Lemma implies Tucker's Lemma - simple combinatorial proof
Sperner’s Lemma is often called the "combinatorial analog" of Brouwer’s Fixed Point Theorem, and similarly Tucker’s Lemma is often called the combinatorial analog of Borsuk–Ulam’s Theorem.
We can ...
15
votes
3
answers
1k
views
Classification of Platonic solids
My question is very basic: where can I find a complete (and hopefully self-contained) proof of the classification of Platonic solids? In all the references that I found, they use Euler's formula $v-e+...
3
votes
1
answer
737
views
Klein Bottle exception to the Heawood Conjecture [duplicate]
Possible Duplicate:
The Klein bottle and the Heawood Conjecture
It is well known that the Heawood Conjecture states that the bound for the number of colours which are sufficient to colour a map ...
2
votes
1
answer
200
views
Subset in $[0,1]^k$ with positive density
Given a positive constant $0<\gamma<1$, does there exists integer $k_0>0$ such that for any integer $k\geq k_0$ the following holds?:
For any $A\subseteq\left[0,1\right]^k$ with the measure ...
0
votes
0
answers
128
views
The smallest dihedral angle of convex polyhedrons
Given a set of points $\{x_{k}\}_{k=0}^{m} \subset \mathbb{R}^n$, is it always possible to find a constant $c=c(m,n)>0$, depending only on the dimension $n$ and the number $m$, such that, after ...