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