cochleoid

A spiral curve that was first studied by J. Peck in 1700 and Bernouilli 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

(x² + y²) 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.

Related category

• PLANE CURVES

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