  By viewing entanglement as a state function, a new kind of phase transition
takes place: the geometric phase transition. This phenomenon occurs due to
singularities in the shape of the entangled states set. It is shown how this
result can be carried to provide a better understanding of the geometry of
entanglement. Surprisingly, this study can be done experimentally, what allows
to determine the shape of different entangled states sets, a purely
mathematical definition, in real experiments.
