Karl Weierstrass showed that given a continuous function $f$ on $[0,1]$ and an epsilon positive, there is a polynomial $p$ such that it is uniformly epsilon close to $f$ on $[0,1]$. In this talk we give a proof of this using coin tossing. We then generalize this to the case of simplexes and hypercubes. We also discuss approximation by $C^{\infty}$ infinity functions using Gauss kernels.
