# Cochleoid

Figure 1. The cochleoid (pdf)

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

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.

#### References

 [1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)
 [a1] J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)
How to Cite This Entry:
Cochleoid. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cochleoid&oldid=30440
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article