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ANGUINEA
Curve studied by L'Hospital and Huygens in 1692, then
by Newton in 1701.
From the Latin anguis "snake, hydra, dragon" (your choice !), name given by Newton. Other name : serpentine cubic. |
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Cartesian equation: Cartesian parametrization: Polar equation: |
The anguinea is the hyperbolism of the circle with respect to a point O of this circle and a straight line parallel to the diameter passing through O. Here, the circle is the circle of diameter [OA] with A(a, 0) and the line, y = d. |
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Like the witch of Agnesi, it is a projection of the horopter. |
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In the figure hereafter, we used
instead of
for more readibility.
The anguinea is a directrix curve of the Plücker's conoid.
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© Robert FERRÉOL 2016