**Cartesian equation: **

*y* = *a* cosh(*x*/*a*)

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The catenary is the shape of a perfectly flexible chain suspended by its ends and acted on by gravity. Its equation was obtained by Leibniz, Huygens and Johann Bernoulli in 1691. They were responding to a challenge put out by Jacob Bernoulli to find the equation of the 'chain-curve'.

Huygens was the first to use the term *catenary* in a letter to Leibniz in 1690 and David Gregory wrote a treatise on the catenary in 1690. Jungius (1669) disproved Galileo's claim that the curve of a chain hanging under gravity would be a parabola.

The catenary is the locus of the focus of a parabola rolling along a straight line.

The catenary is the evolute of the tractrix. It is the locus of the mid-point of the vertical line segment between the curves *e*^{x} and *e*^{-x}.

Euler showed in 1744 that a catenary revolved about its asymptote generates the only minimal surface of revolution.

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JOC/EFR/BS January 1997

The URL of this page is:

http://www-history.mcs.st-andrews.ac.uk/Curves/Catenary.html