Definition:Tractrix

Definition

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Definition 1

The tractrix is the plane curve which is the involute of the catenary.

Definition 2

Let $S$ be a cord situated as a (straight) line segment whose endpoints are $P$ and $T$.

Let $T$ be dragged in a direction perpendicular to the straight line in which $S$ is aligned.

The curve along which $P$ travels is known as a tractrix.

Definition 3

The tractrix is the locus of a point such that the length $PT$ of the tangent at $P$ to where it intersects the $x$-axis at $T$ is constant.

Axis

The axis of a tractrix is the straight line aligned with the initial position of the line segment being dragged.

Asymptote

The asymptote of a tractrix is the straight line along which the end of the line segment is being dragged.

Also defined as

The tractrix can also be defined with respect to the $y$-axis:

The tractrix is the locus of a point such that the length $PT$ of the tangent at $P$ to where it intersects the $y$-axis at $T$ is constant.

Also see

• Equivalence of Definitions of Tractrix
• Definition:Pursuit Curve, of which the tractrix is an example

• Results about the tractrix can be found here.

Internationalization

Tractrix is translated:

In German:

hundkurve

(literally: dog curve)

(that is: the path taken by a dog chasing its prey)

Historical Note

The tractrix was first investigated by Claude Perrault in $1670$.

It was later studied by Isaac Newton in $1676$ and Christiaan Huygens in $1692$.

Jacob Bernoulli also gave some time to it.

Linguistic Note

The word tractrix derives from the Latin traho (trahere, traxi, tractum) meaning to pull or to drag.

The plural is tractrices.

Sources

• Weisstein, Eric W. "Tractrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Tractrix.html