Cochleoid

A concheloid with a = 1

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

$x=\frac{a\sin t\cos t}{t}$

$y=\frac{a\sin^2 t}{t}$

References

• J. Dennis Lawrence (1972). A catalog of special plane curves. Dover Publications. p. 192. ISBN 0-486-60288-5.