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Catenary facts for kids

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Kette Kettenkurve Catenary 2008 PD
A chain hanging from points forms a catenary.

In physics and geometry, a catenary (US /ˈkætənˌɛri/, UK /kəˈtnəri/) 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, but it is not a parabola: it is a (scaled, rotated) graph of the hyperbolic cosine. The curve 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 materials sciences, funicular.

The silk on a spider's web forming multiple elastic catenaries.

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, specifically a minimal surface of revolution. 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.

Freely-hanging electric power cables (especially those used on electrified railways) can also form a catenary.

Catenaries and related curves are used in architecture and engineering, in the design of bridges and arches, so that forces do not result in bending moments. In the offshore oil and gas industry, "catenary" refers to a steel catenary riser, a pipeline suspended between a production platform and the seabed that adopts an approximate catenary shape. The word "catenary" comes from the Latin word catena, which means "chain". A catenary is also called called an alysoid and a chainette.

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