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.

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