  We study the space geometry of a rotating disk both from a theoretical and
operational approach, in particular we give a precise definition of the space
of the disk, which is not clearly defined in the literature. To this end we
define an extended 3-space, which we call relative space: it is recognized as
the only space having an actual physical meaning from an operational point of
view, and it is identified as the 'physical space of the rotating platform'.
Then, the geometry of the space of the disk turns out to be non Euclidean,
according to the early Einstein's intuition; in particular the Born metric is
recovered, in a clear and self consistent context. Furthermore, the
relativistic kinematics reveals to be self consistent, and able to solve the
Ehrenfest's paradox without any need of dynamical considerations or ad hoc
assumptions.
