Tractrix or Pursuit
Curve
The inverse
Hyperbolic secant can be used to define a curve called a tractrix
or pursuit curve.
The
tractrix is sometimes called a tractory or equitangential curve.
It was first studied by Huygens
in 1692 who gave it its name. Later Leibniz,
Johann
Bernoulli and others studied the curve.
The study of the
tractrix started with the following problem being posed to Leibniz:
What is the path
of an object dragged along a horizontal plane by a string of
constant length when the end of the string not joined to the
object moves along a straight line in the plane?
He solved this using
the fact that the axis is an asymptote to the tractrix.
The highlighted
sentences are from this link: http://wwwgap.dcs.stand.ac.uk/~history/Curves/Tractrix.html
A link to a program
for calculating Tractrix: Tractrix
Contour Calculator
