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Topic: Catenary

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	Catenary Summary
		In 1691, Leibniz, Christiaan Huygens, and Johann Bernoulli derived the equation in response to a challenge by Jakob Bernoulli.
		A kiln, a kind of oven for firing pottery, may be made from firebricks with a body in the shape of a catenary arch, usually nearly as wide as it is high, with the ends closed off with a permanent wall in the back and a temporary wall in the front.
		In semi-rigid airships, a catenary curtain is a fabric and cable internal structure used to distribute the weight of the gondola across a large area of the ship's envelope.
	www.bookrags.com /Catenary (1581 words)

	Catenary - LoveToKnow 1911
		The simple catenary is shown in the figure.
		the catenary solves the problem: to find a curve joining two given points, which when revolved about a line co-planar with the points traces a surface of minimum area (see Variations, Calculus Of).
		x The involute of the catenary is called the tractory, tractrix or antifriction curve; it has a cusp at the vertex of the catenary, and is asymptotic to the directrix.
	www.1911encyclopedia.org /Catenary (326 words)

	Catenary Arch
		Catenary Arch is an arch assembled out of numbered blocks.
		In spite of the fact that the blocks are relatively slender, they can stand due to their catenary shape.
		The mathematical formulae for the catenary are also presented.
	www.exploratorium.edu /cmp/exhibits/c/catenary.html (104 words)

	Fidelio Article - Schiller Institute- LEIBNIZ on the Catenary Spring 2001 issue
		Leibniz's paper on the catenary curve, was written at the instigation of Jacques Bernoulli for the Acta Eruditorum of Leipzig, June 1691.
		Conversely, if the catenary curve is physically constructed, by suspending a string, or a chain, you can construct from it as many proportional means as you wish, and find the logarithms of numbers, or the numbers of logarithms.
		Thus, the logarithmic curve is the geometric mean of the catenary curve, and the catenary curve is the arithmetic mean of the logarithmic curve.
	www.schillerinstitute.org /fid_97-01/011_catenary.html (3602 words)

	Catenary
		Catenary (also known as chainette, alysoid, and hyperbolic cosine) is defined as the curve of the function Cosh[x].
		The Catacaustic of the exponential curve E^x with light rays from above and parallel to the y axes is the catenary.
		The radial of catenary is the Kampyle of Eudoxus.
	xahlee.org /SpecialPlaneCurves_dir/Catenary_dir/catenary.html (635 words)

	PlanetMath: catenary
		The arc length of the catenary (2) from the apex
		The radius of curvature of the catenary (2) is
		This is version 17 of catenary, born on 2005-06-07, modified 2007-01-19.
	planetmath.org /encyclopedia/Catenary.html (281 words)

	Catenary - Wikipedia, the free encyclopedia
		In 1691, Leibniz, Christiaan Huygens, and Johann Bernoulli derived the equation in response to a challenge by Jakob Bernoulli.
		A kiln, a kind of oven for firing pottery, may be made from firebricks with a body in the shape of a catenary arch, usually nearly as wide as it is high, with the ends closed off with a permanent wall in the back and a temporary wall in the front.
		In semi-rigid airships, a catenary curtain is a fabric and cable internal structure used to distribute the weight of the gondola across a large area of the ship's envelope.
	en.wikipedia.org /wiki/Catenary (1159 words)

	Xah: Special Plane Curves: catenary
		Catenary (also known as chainette, alysoid, and hyperbolic cosine) is defined as the curve of the function Cosh[x].
		The Catacaustic of the exponential curve E^x with light rays from above and parallel to the y axes is the catenary.
		The radial of catenary is the Kampyle of Eudoxus.
	www.xahlee.org /SpecialPlaneCurves_dir/Catenary_dir/catenary.html (678 words)

	stehvelo's z trains - installing catenary (Site not responding. Last check: )
		A second transformer is needed to provide current to the catenary and that means two locomotives can be run simultaneously and independently on the same section of track - one controlled by current from the overhead system and the other controlled with power from the rails.
		Catenary sections no longer touch each other in these larger nylon clips, so the copper contact is essential to transmit current.
		One solution is to remove both catenary and clip once again and shave a tiny amount of material from the underside of the clip with a sharp knife.
	www.kolumbus.fi /stephenb/z/catenary.htm (2372 words)

	Catenary -- from Wolfram MathWorld
		The slope is proportional to the arc length as measured from the center of symmetry.
		-gon, the Cartesian equation of the corresponding catenary is
		Gray, A. "The Evolute of a Tractrix is a Catenary." §5.3 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed.
	mathworld.wolfram.com /Catenary.html (392 words)

	An Ancient Egyptian Catenary Construction Curve
		The catenary can also be created in the form of an arch, and offers a very rigid structure.
		The difference between the coordinate values specified by the ancient architect and the theoretical catenary is four fingers for one point, three for another, and the rest less than two.
		Several of the points are almost directly on the theoretical, within the ability of the architect to specify by the number of fingers.
	www.egyptorigins.org /catenarycurve.htm (839 words)

	CATENARY FOR STEAM RAILROAD ELECTRIFICATION (Site not responding. Last check: )
		Catenary was needed to carry the current and to hold the contact wire level.
		Any sort of catenary, from a type with a great deal of sag, to a type with very little sag can be modeled by adjusting the tension on the messenger wire, with the tuning gear.
		With inclined catenary, the messenger wire is off-set to the outside of the curve.
	webhome.idirect.com /~helmutw/milwrd/models/cat.htm (5217 words)

	catenary
		When x is slightly greater than three however, the catenary begins to rapidly outgrow the value of the parabola.
		If a parabola is rolled along a straight line, the focus of the parabola moves along a catenary curve.
		The St. Louis Arch, which is 630 feet (192 meters) wide at the base and 630 feet tall, follows the form of a catenary, the exact formula for which is displayed inside the arch: y = 68.8 cosh (0.01x -1), where cosh is the hyperbolic cosine function.
	www.daviddarling.info /encyclopedia/C/catenary.html (282 words)

	The Shape of a Catenary
		The figure crudely represents a catenary, or the shape of a perfectly flexible, uniform cord that is suspended between two points.
		The object is to determine both the catenary’s shape and its length.
		This rationale is somewhat less than satisfying, however, since the plots of the parabola and the "exact" catenary appear so close together that it’s hard to believe the difference in length shown in the table.
	mathforum.org /calcpow/images/catenarytextexact.htm (506 words)

	tents with catenary ridgeline - WhiteBlaze
		The catenary is the shape of a perfectly flexible chain suspended by its ends and acted on by gravity.
		Derived from the Latin word meaning “chain”, a catenary curve is the sag of a cord hung from both endpoints.
		A catenary curve is often used to achieve maximum structural stength and is used with some tents to achieve maximum wind loading as a structure.
	www.whiteblaze.net /forum/showthread.php?t=6973 (1024 words)

	Catenary
		The catenary is the shape of a perfectly flexible chain suspended by its ends and acted on by gravity.
		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.
		The catenary is the evolute of the tractrix.
	www-groups.dcs.st-and.ac.uk /~history/Curves/Catenary.html (180 words)

	Tarptent Ultralight Shelters Catenary Curve Design
		Catenary curves are formed when a homogeneous cable is suspended by its endpoints.
		The word catenary is derived from the Latin word for "chain." The mathematics of the curves are described by a hyperbolic function.
		Catenary curves can also be seen in several famous architectural structures.
	www.tarptent.com /catenary.html (58 words)

	Philadelphia Museum of Art - Information : Press Room : Press Releases : 2001
		The Museum is acquiring Catenary (I Call to the Grave) through funds contributed in part by its Committee on Modern and Contemporary Art and other generous donors in honor of the 125th anniversary of the Museum in 2001.
		The word "catenary," a term usually associated with suspension bridges, describes the curve imposed on the suspended string by the force of gravity.
		Catenary (I Call to the Grave) also joins an important group of paintings and sculptures that have been on loan to the Museum from the artist for many years.
	www.philamuseum.org /press/releases/2001/260.html (1002 words)

	The Utility of Catenaries to Electric Utilities
		The graph of the catenary is shown in blue.
		The poles have height h and the minimum value of the catenary function is c + a.
		In the context of the catenary function, we can interpret the length of the wire as the arc length of the graph of f from x = -s to x = s.
	mathdemos.gcsu.edu /mathdemos/catenary/catenary.html (1271 words)

	Catenary Road and Square Wheels
		Since the length of each catenary curved section of the road exactly equals the length of one side of the square, the corners of the square always end up rolling over the low points of the road and the midpoints of the sides always roll over the high points of the road.
		We began by turning the road upside down, hanging an 8 inch long chain between two points on the edge of the foam and tracing the catenary arch which was formed.
		This exhibit can be used to study the geometry of catenary curves in math classes and the concept of center of gravity in physics.
	nths.newtrier.k12.il.us /academics/math/Connections/curves/sqwheels.htm (375 words)

	CATENARY HOSE
		Catenary hoses are designed to provide the crude oil loading line from Floating Production and Storage vessels, permanently moored at offshore installations, to the shuttle tankers which visit them.
		Derivatives within the catenary hose range include hoses with integrally built in buoyancy, sufficient to ensure that the hose line would not be lost if cast off from the F.P.S.O. during an emergency, even if full of water, and hoses finished with an outer cover of tough, low friction polyurethane.
		All our catenary hoses are custom built for individual systems and we welcome early involvement in new projects so that we can determine and recommend the best hose line for the purpose.
	www.parker.com /euroitr/offshore/catenary.asp (378 words)

	Scaffolding eTool: Suspended Scaffolds: Catenary
		A catenary scaffold is a scaffold consisting of a platform supported by two essentially horizontal and parallel ropes attached to structural members of a building or other structure.
		Each employee on a catenary scaffold must be protected by a personal fall-arrest system.
		Catenary scaffolds have a maximum intended load of 500 pounds.
	www.osha.gov /SLTC/etools/scaffolding/suspended/catenary.html (205 words)

	Catenary tarps, tarp-tents, and tents
		The word "catenary" is latin derived, and originally referred to the curved shape of a length of chain suspended from both ends.
		The only thing they lacked was the trendy term "catenary." And by the way, they thrived quite nicely - for perhaps millions of years - without our modern gear which we consider so essential.
		Like all tarps and tents, it is the catenary type, as evidenced by the curve of its walls.
	www.ray-way.com /tb/catenary/catenary.php (2578 words)

	Cable Sag Error (Catenary Curve Effect) Calculator
		A catenary curve describes the shape the displacement cable takes when subjected to a uniform force such as gravity.
		The equation was obtained by Leibniz and Bernoulli in 1691 in response to a challenge by Bernoulli and Jacob.
		The length of the cable is the catenary length from point -l/2 to point l/2 (formula 14).
	www.spaceagecontrol.com /calccabl.htm (1027 words)

	Viessmann - HO Scale Catenary
		The Viesmann catenary requires no smoldering, simply clip it in place and start operating.
		Viesmann has found the way to make catenary installation simple, realistic and functional.
		Forget about those other catenary systems that require soldering and complicated setup.
	www.reynaulds.com /viessmann/v_ho_catenary.asp?item=lngNumericSort (97 words)

	Definition of catenary - Merriam-Webster Online Dictionary
		Learn more about "catenary" and related topics at Britannica.com
		Find more about "catenary" instantly with Live Search
		See a map of "catenary" in the Visual Thesaurus
	www.m-w.com /cgi-bin/dictionary?book=Dictionary&va=catenary (81 words)

	Funicular
		All we have is a sentence that is equivalent to "catenary".
		We must remember that the curve of a cable is a catenary only if the cable has no stiffness and is uniform throughout its length.
		The funicular for the catenary is not exactly central in the diagram because of the crude method of iterating in the calculation.
	www.brantacan.co.uk /funicular.htm (2680 words)

	catenary
		A bridge, constructed as a catenary with exactly sawn wooden blocks, moves in the same manner as the chain, without breaking down.
		When a sail is attached on two horizontal bars, and the wind blows in a direction perpendicular to the bars, a catenary formed sail occurs.
		In 1819 a building was erected in 1819, with the form of a catenary.
	www.2dcurves.com /exponential/exponentialhc.html (473 words)

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