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Ophiuride


Ophiuride
Ophiuride

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

 x(x^2+y^2)+(ax-by)y=0,
(1)

where a>0,b>=0, or by the polar equation

 r=(bsintheta-acostheta)tantheta,
(2)

for -pi/2<t<pi/2. The curve is named base on its resemblance to a particular species of star-fish (right figure). Taking a=0 yields a cissoid of Diocles.

Its curvature is

 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)

See also

Cissoid of Diocles

This entry contributed by Margherita Barile

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References

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

Referenced on Wolfram|Alpha

Ophiuride

Cite this as:

Barile, Margherita. "Ophiuride." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Ophiuride.html

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