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
and in polar coordinates by
The points of contact of parallel tangents to the cochleoid lie on a strophoid.
Related category PLANE CURVES
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