Is there a simple way to prove the Brouwer fixed Point theorem?

Question

The quest may be for references but I want to know if there is a simple way to prove the Brouwer fixed point theorem!

That is if a function $f:\bar{B}\to\bar{B}$ is continuous then $f$ admits one fixed point!

The answer for the $R¹$ is a real analysis exercise and it also holds for any interval compact!

The proof is related with Schauder fixed-point theorem?

Answer 1

There is a book proof using Sperner's Lemma which is (very!) elegant and (IMO) simple.