Thomas rotation and Foucault pendulum under a simple unifying geometrical point of view

In this paper we show that there is a complete parallelism between the Foucault pendulum and the Thomas rotation phenomena by using the concept of parallel transport in a surface. In the case of the Foucault pendulum the surface is the ordinary sphere corresponding to the Earth sphere, whereas in the case of the Thomas rotation the surface is the pseudosphere corresponding to the space of relativistic velocities. Moreover, in both cases we use a simple method that reduces the problem to the parallel transport in a conical surface, and so, to the plane.