The lituus is a species of the Archimedean spiral.
Some authors add (-r, φ) forming a double shape.

The curve is formed by the loci of a point P moving in such a way that the area of a circular sector remains constant.

Roger Cotès (1682-1716) was the first to study the curve. Appointed professor at Cambridge at the age of 24 his work was published only after his death.

Maclaurin gave the curve its name in his book 'Harmonia Mensurarum' (1722) using the resemblance of the curve to a crosier 1).

The inverse of the curve is Fermat's spiral.


1) lituus (Lat.) = bend, crook.
In the old Roman empire the lituus was a crosier.