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
![画像: 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)).](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/Ophiuride/NumberedEquation3.svg){kind=link}
See also
Cissoid of DioclesThis 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
OphiurideCite this as:
Barile, Margherita. "Ophiuride." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Ophiuride.html