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OPHIUROID

Curve studied by Uhlhorn in 1809.
From the Greek ophis "snake" and oura "tail". |

Polar equation: .
Cartesian equation: . Rational circular cubic with a double point. |

Like all rational
circular cubics, the ophiuroids have three geometrical definitions.
They are:

- the cissoids with pole *O* of a circle (*C*)
passing by *O* and a line (*D*) the symmetric image about *O*
of which passes by *A*, the point diametrically opposed to *O*
(here, *A*(*a*, *b*) and (*D*): *x* = – *a*).

Note that the right ophiuroid is none other than the cissoid of Diocles.

Real ophiuroids!

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© Robert FERRÉOL 2017