# cochleoid

A cochleoid is a spiral curve that was first studied by J. Peck in 1700 and Bernoulli in 1726. Its name, meaning "snail-form" (kochlias is Greek for "snail"), was coined by Benthan and Falkenburg in 1884.

The cochleoid can be constructed as follows: given a point *O* and
the *y*-axis. For all circles through *O* (hence tangent to
the *y*-axis), place a constant distance on the circle. The collection
of these points is the cochleoid. In Cartesian coordinates, it is given
by the formula

(*x*^{ 2} + *y*^{ 2}) tan^{-1}(*y*/*x*)
= *ay*

and in polar coordinates by

*r* = *a* sin*θ* / *θ*

The points of contact of parallel tangents to the cochleoid lie on a strophoid.