TITLE: Is there a simple way to prove the Brouwer fixed Point theorem?
QUESTION [6 upvotes]: 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?

REPLY [9 votes]: There is a book proof using Sperner's Lemma which is (very!) elegant and (IMO) simple.