  We present a didactic derivation of the special theory of relativity in which
Lorentz transformations are `discovered' as symmetry transformations of the
Klein-Gordon equation. The interpretation of Lorentz boosts as transformations
to moving inertial reference frames is not assumed at the start, but it
naturally appears at a later stage. The relative velocity $\textbf{v}$ of two
inertial reference frames is defined in terms of the elements of the pertinent
Lorentz matrix, and the bound $|\textbf{v}| <c\;$ is obtained as a simple
theorem that follows from the structure of the Lorentz group. The polar
decomposition of Lorentz matrices is used to explain noncommutativity and
nonassociativity of the relativistic composition (`addition') of velocities.
