  This article presents a brief historical review of G. I. Taylor's solution of
the point blast wave problem which was applied to the Trinity test of the first
atomic bomb. Lie group symmetry techniques are used to derive Taylor's famous
two-fifths law that relates the position of a blast wave to the time after the
explosion and the total energy released. The theory of exterior differential
systems is combined with the method of characteristics to demonstrate that the
solution of the blast wave problem is directly related to the basic
relationships that exist between the geometry (or symmetry) and the physics of
wave propagation through the equations of motion. The point blast wave model is
cast in terms of two exterior differential systems and both systems are shown
to be integrable with local solutions for the velocity, pressure, and density
along curves in space and time behind the blast wave.
