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A chain hanging from points forms a catenary. The silk on a spider's web forming multiple elastic catenaries.. In physics and geometry, a catenary (US: / ˈ k æ t ən ɛr i / KAT-ən-err-ee, UK: / k ə ˈ t iː n ər i / kə-TEE-nər-ee) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field.
Catenary: An arched roof in the form of a catenary curve. Arched roof, bow roof, [11] Gothic, Gothic arch, and ship's bottom roof. Historically also called a compass roof. [12] [13] Circular Bell roof (bell-shaped, ogee, Philibert de l'Orme roof): A bell-shaped roof. Compare with bell-cast eaves. Domed; Onion dome or rather an imperial roof ...
The Gateway Arch is a weighted catenary: thick at the bottom, thin at the top.. A weighted catenary (also flattened catenary, was defined by William Rankine as transformed catenary [1] and thus sometimes called Rankine curve [2]) is a catenary curve, but of a special form: if a catenary is the curve formed by a chain under its own weight, a weighted catenary is the curve formed if the chain's ...
A mudbrick catenary arch A catenary curve (left) and a catenary arch, also a catenary curve (right). One points up, and one points down, but the curves are the same. A catenary arch is a type of architectural arch that follows an inverted catenary curve. The catenary curve has been employed in buildings since ancient times.
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
The practical designs for bridges are somewhere in between, and thus use the curves that represent a compromise that combines both the catenary and the funicular curve for particular non-uniform distribution of load. [83] The practical free-standing arches are stronger and thus heavier at the bottom, so a weighted catenary curve is utilized for ...
The envelope of the normals of the tractrix (that is, the evolute of the tractrix) is the catenary (or chain curve) given by y = a cosh x / a . The surface of revolution created by revolving a tractrix about its asymptote is a pseudosphere. The tractrix is a transcendental curve; it cannot be defined by a polynomial equation.
Unlike simple overhead wires, in which the uninsulated wire is attached by clamps to closely spaced crosswires supported by poles, catenary systems use at least two wires. The catenary or messenger wire is hung at a specific tension between line structures, and a second wire is held in tension by the messenger wire, attached to it at frequent ...