Some notes on the relativistic Doppler effect

The properties of the analytical formula of the relativistic Doppler-effect are discussed from the geometric standpoint. It is shown, in particular, that, contrary to the widely accepted view, as the observer and the source of electromagnetic radiation approach one another, in addition to the violet shift also a zero and a red shift (z ≥ 0) can be observed depending on the angle θ between the vector of relative velocity β and the observation direction.