In physics and geometry, the catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends. The curve has a U-like shape, superficially similar in appearance to a parabola (though mathematically quite different). It also appears in the design of certain types of arches and as a cross section of the catenoid -- the shape assumed by a soap film bounded by two parallel circular rings.
The catenary is also called the "alysoid", "chainette", or, particularly in the material sciences, "funicular".
Mathematically, the catenary curve is the graph of the hyperbolic cosine function. The surface of revolution of the catenary curve, the catenoid, is a minimal surface, and is the only minimal surface of revolution other than the plane. The mathematical properties of the catenary curve were first studied by Robert Hooke in the 1670s, and its equation was derived by Leibniz, Huygens and Johann Bernoulli in 1691.
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August 7th, 2012
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