# Lituus (mathematics)

This article is about spiral. For Roman wand, see Lituus.

In mathematics, a **lituus** is a spiral with polar equation

where *k* is any non-zero constant.
Thus, the angle θ is inversely proportional to the square of the radius r.

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

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.

## External links

- Hazewinkel, Michiel, ed. (2001), "Lituus",
*Encyclopedia of Mathematics*, Springer, ISBN 978-1-55608-010-4 - Weisstein, Eric W. "Lituus".
*MathWorld*.

- Interactive example using JSXGraph
- O'Connor, John J.; Robertson, Edmund F., "Lituus",
*MacTutor History of Mathematics archive*, University of St Andrews.

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