  In \cite{GCF} it is proved that any quadratic irrational number has a
representation as a continuous, infinite and periodic fraction. In 1848,
Charles Hermite through a letter Jacobi \cite{Per} wondered if this fact could
be generalized to cubic irrational numbers. In This research addresses the
Hermite problem, through the study of continuous functions by pieces associated
to Fuchsian Groups, particularly a function $f_\Gamma$ associated to the Group
Modular $\Gamma$, which was raised in 1978 by Robert Edward and Caroline
Series, with this function it is find a representation as infinite periodic
continued fraction for irrational numbers quadratics and non-periodic infinite
for non-quadratic irrationals.
  Keywords: Dynamic Approximation, Fuchsian Groups, Hermite Problem.
