In this paper, we show that redshifts, which appear in some pedagogical examples, can be expressed
in terms of the Doppler–Fizeau effect. For this purpose, we use, as suggested by Weyl, the worldline
elements of two physical events: the emission and the reception of a monochromatic wave. The
redshift in special relativity and its Galilean approximation are derived in a simpler way than is
usually done. In general relativity, the cosmological redshift can be obtained with the general Weyl
formula in three important cases of gravitational fields, even though the gravitational redshift,
due to bodies running away from each other, cannot be reduced to a simple kinematic effect.