Two exact derivations of the mass/energy relationship, E=mc^2
  The E=mc^2 relationship is not unique to special relativity. Einstein published one exact derivation from special relativity and two approximate derivations that used general extensions to Newtonian mechanics, and an exact derivation is also possible if we use a "first-order" Doppler equation instead of special relativity's "relativistic Doppler" formula. We present two sample derivations based on different non-transverse Doppler relationships, and briefly look at the two diverging systems of physics that result. 
Eric Baird