This spiral is a generalization of Archimedes' spiral
(a=1), named to the Greek Archimedes (225 BC).
The inverse of the spiral with a constant a is an
Archimedean spiral with a constant -a.
There are some special situations:
An Archimedean spiral with parameter a has as polar
inverse an Archimedean spiral with parameter -a: so the lituus and
Fermat's spiral are
inversely related, and also the hyperbolic and the Archimedes' spiral.
It was Sacchi (1854) who distinguished this group of spirals, for the first time.