Ophiuride

The ophiuride is a cubic curve (left figure) given by the implicit equation

(1)

where , or by the polar equation

(2)

for . The curve is named base on its resemblance to a particular species of star-fish (right figure). Taking yields a cissoid of Diocles.

$kappa(t)=(2{a^2-3b^2+bsec^2t[3b-asectsin(3t)]})/({a^2-3b^2+b^2[2+cos(2t)]sec^4t-4abtant}^(3/2)).$

(3)

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Shikin, E. V. Handbook and Atlas of Curves. Boca Raton, FL: CRC Press, pp. 266-267, 1995.