  There are several ways to derive Einstein's celebrated formula for the energy
of a massive particle at rest, $E=mc^2$. Noether's theorem applied to the
relativistic Lagrange function provides an unambiguous and straightforward
access to energy and momentum conservation laws but those tools were not
available at the beginning of the twentieth century and are not at hand for
newcomers even nowadays. In a pedestrian approach, we start from relativistic
kinematics and analyze elastic and inelastic scattering processes in different
reference frames to derive the relativistic energy-mass relation. We extend the
analysis to Compton scattering between a massive particle and a photon, and a
massive particle emitting two photons. Using the Doppler formula, it follows
that $E=\hbar \omega$ for photons at angular frequency $\omega$ where $\hbar$
is the reduced Planck constant. We relate our work to other derivations of
Einstein's formula in the literature.
