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 ex 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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