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.