  It is known that the Burau representation of the 4-strand braid group is
faithful if and only if certain matrices f and k generate a (non-abelian) free
group. Regarding f and k as isometries of a euclidean building we show that f^3
and k^3 generate a free group. We give two proofs, one utilizing the metric
geometry of the building, and the other using simplicial retractions.
