# Lituus (mathematics)

## Spiral / From Wikipedia, the free encyclopedia

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

This article relies largely or entirely on a single source. (May 2024) |

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

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

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.