# Cochleoid

From Encyclopedia of Mathematics

A plane transcendental curve whose equation in polar coordinates is \begin{equation} \rho = a\frac{\sin\varphi}{\varphi}. \end{equation}

The cochleoid has infinitely many spirals, passing through its pole and touching the polar axis (see Fig.). The pole is a singular point of infinite multiplicity. Any straight line through the pole $O$ intersects the cochleoid; the tangents to the cochleoid at these intersection points pass through the same point.

The inverse of the cochleoid with respect to the origin is the quadratrix of Hippias.

#### References

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

[a1] | J.D. Lawrence, "A catalog of special plane curves" , Dover (1972) ISBN 0-486-60288-5 Zbl 0257.50002 |

**How to Cite This Entry:**

Cochleoid.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Cochleoid&oldid=54740

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