Brenti and Welker have shown that for any simplicial n-dimensional complex X, the f-vectors of successive barycentric subdivisions of X have roots which converge to fixed values depending only on the dimension of X. In this talk, we will present this result, sketching a new, simple, and intuitive geometric proof. Moreover, we will discuss generalizations of this result, computations of these limit values, and show an interesting symmetry of the limit values about the real number -2. This is based on joint work with Emanuele Delucchi and Aaron Pixton.