Definition:Tractrix

Definition

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.

Also see

The tractrix is an example of a pursuit curve.

Linguistic Note

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

The plural is tractrices.

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.

Sources

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 11$: Special Plane Curves: Tractrix: $11.21$
• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 2.12$: The Hanging Chain. Pursuit Curves: Example $(2)$