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KÜLP QUARTIC

Curve studied by Külp in 1868 (archiv
der Math. und Physik p. 97) and Goormaghtigh
in 1913.
Ludwig Külp (1835 - 1891) : German physiker. Other name: Külp conchoid (because of its resemblance to the conchoid of Nicomedes). |

Cartesian parametrization: .
Cartesian equation: i.e. . Rational quartic. |

The Külp quartic is the hyperbolism of the circle with respect to its centre and a tangent (special case of Granville egg).

Here, the circle is the circle with diameter [*OA*]
where *A*(0, *a*) and the line is *y* = *a*.

The Külp quartic is also the projection on the plane
*xOy*
of the biquadratic,
intersection of the cylinder
of revolution
and of the hyperbolic
paraboloid.

This curve must not be mistaken for the quartic with polar equation and Cartesian equation which is very similar to it:

Compare to the witch
of Agnesi.

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© Robert FERRÉOL 2017