  The Argand diagram is used to display some characteristics of the Riemann
Zeta function. The zeros of the Zeta function on the complex plane give rise to
an infinite sequence of closed loops, all passing through the origin of the
diagram. This leads to the analogy with the scattering amplitude, and an
approximate rule for the location of the zeros. The smooth phase of the Zeta
function along the line of the zeros is related to the quantum density of
states of an inverted oscillator.
