4
votes
0answers
303 views

Equivalence of Brouwers fixed point theorem and Sperner's lemma

I'm looking for a proof that Brouwer's fixed point theorem implies Sperner's lemma. All proof I've found just prove that there must be at least one completely colored n-simplex, not that there must be ...
4
votes
1answer
149 views

Is there any way to give sense to a geometric/visual proof?

Suppose one is given the following visual proof that $$\lim\limits_{n \to \infty} \sum_{k=1}^n \frac{1}{2^k} = 1$$ which is the following construction over $[0,1]\times[0,1]$ What this is ...