Cochleoid
# Cochleoid

In geometry, a cochleoid is a snail-shaped curve similar to a strophoid which can be represented by the polar equation

    $r={\frac {a\sin \theta }{\theta }},$

the Cartesian equation

    $(x^{2}+y^{2})\arctan {\frac {y}{x}}=ay,$

or the parametric equations

    $x={\frac {a\sin t\cos t}{t}},\quad y={\frac {a\sin ^{2}t}{t}}.$

The cochleoid is the inverse curve of Hippias' quadratrix.

