Definition:Tractrix/Definition 2
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 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
- Results about the tractrix can be found here.
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
- 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 $(2)$
- 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 9$: Special Plane Curves: Tractrix: $9.21.$
- Weisstein, Eric W. "Tractrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Tractrix.html