Lituus (mathematics)

The lituus spiral (/ˈlɪtju.əs/) is a spiral in which the angle θ is inversely proportional to the square of the radius r.

This spiral, which has two branches depending on the sign of r, is asymptotic to the x axis. Its points of inflexion are at

${\displaystyle (\theta ,r)=\left({\tfrac {1}{2}},\pm {\sqrt {2k}}\right).}$

The curve was named for the ancient Roman lituus by Roger Cotes in a collection of papers entitled Harmonia Mensurarum (1722), which was published six years after his death.