# Lituus

From Encyclopedia of Mathematics

A plane transcendental curve whose equation in polar coordinates is

$$\rho=\frac{a}{\sqrt\phi}.$$

To every value of $\phi$ correspond two values of $\rho$, one positive and one negative. The curve consists of two branches, that both approach the pole asymptotically (see Fig.). The line $\phi=0,\phi=\pi$ is an asymptote at $\rho=\pm\infty$, and $(1/2,a\sqrt2)$ and $(-1/2,-a\sqrt2)$ are points of inflection. The lituus is related to the so-called algebraic spirals.

#### References

- [1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)

#### References

[a1] | K. Fladt, "Analytische Geometrie spezieller ebener Kurven" , Akad. Verlagsgesell. (1962) |

[a2] | F. Gomes Teixeira, "Traité des courbes" , 1–3 , Chelsea, reprint (1971) |

**How to Cite This Entry:**

Lituus.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Lituus&oldid=52722

This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article