Cochleoid

${\displaystyle r={\frac {\sin \theta }{\theta }},-20<\theta <20}$

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.