The
study of this curve started with a problem stated by Huygens (1692): given a
inextensible string, moving in a straight line, dragging an object. What then, is the path
of that object, asked Huygens himself. And he gave the curve the name of the tractrix.
Also Leibniz and Johann Bernoulli studied the curve.
Because the dragging quality the curve has been given the names drag curve^{1)}
and tractory curve. Also the name of donkey curve^{2)} can be heard.
For the tractrix the length of a tangent from the tangent point to the asymptote is constant, leading to its alternative name of equitangential curve.
The curve must not be confused with the pursuit curve, while there is no fixed length between dragging and dragged object.
Relationships with other curves are the following:
Beltrami (1868) used the tractrix to rotate around its asymptote, in his study
of nonEuclidean geometry. The surface of the resulting pseudosphere has a constant
negative curvature.
notes
1) trahere (Lat.) = to drag
In German: Schleppkurve.
2) In French: courbe de l'âne
