# Is there an easy derivation of relativistic velocities addition and relativistic doppler shift?

Is there an easy derivation of relativistic velocities addition and relativistic doppler shift?

I'm looking for some easy derivation of the above. Like this http://www.sparknotes.com/physics/specialrelativity/kinematics/section2.rhtml. I'm looking for derivations without needing to use the Lorentz transformations.

-
 Your example from sparknotes is using the invarience of the proper time, but this implies the Lorentz transformations and vice versa so it's really the same calculation. We usually teach students the Lorentz transformations because mistakes in algebra aside it's hard to go wrong with them. With the sort of argument in the sparknotes example it's easy to make conceptual errors. – John Rennie Nov 11 '12 at 15:36