Archimedean spiral


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.