I'm looking for a proof that Brouwer's fixed point theorem implies Sperner's lemma. The proof should be understandable by an undergraduate.
Thanks in advance!
A simple proof can be found in a paper by Park and Jeong:
A PROOF OF THE SPERNER LEMMA FROM THE BROUWER FIXED POINT THEOREM Nonlinear Analysis Forum 8(1), pp. 65–67, 2003 (available from http://www.na-forum.org/)