Cartesian equation: y = a cosh(x/a)
Click below to see one of the Associated curves.
Definitions of the Associated curves Evolute Involute 1 Involute 2 Inverse curve wrt origin Inverse wrt another circle Pedal curve wrt origin Pedal wrt another point Negative pedal curve wrt origin Negative pedal wrt another point Caustic wrt horizontal rays Caustic curve wrt another point
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
and e
.
Euler showed in 1744 that a catenary revolved about its asymptote generates the only minimal surface of revolution.
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