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Topic: Tautochrone

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	Tautochrone curve (Site not responding. Last check: 2007-11-05)
		A tautochrone curve is the curve for which the time taken by a particle sliding down it under uniform gravity to its lowest point is independent of its starting point.
		The tautochrone problem, the attempt to identify this curve, was solved by Huygens in 1659.
		He proved geometrically in his Horologium oscillatorium (The Pendulum Clock, 1673) that the curve was a cycloid.
	www.encyclopedia-1.com /t/ta/tautochrone_curve.html (103 words)

	Tautochrone curve - Wikipedia, the free encyclopedia
		A tautochrone or isochrone curve is the curve for which the time taken by a particle sliding down it under uniform gravity to its lowest point is independent of its starting point.
		The time is equal to π times the square root of the radius over the gravitation constant.
		The tautochrone problem, the attempt to identify this curve, was solved by Christiaan Huygens in 1659.
	www.wikipedia.org /wiki/Tautochrone (139 words)

	The History of Curvature (Site not responding. Last check: 2007-11-05)
		This, combined with the fact that the cycloid is a tautochrone, led to Huygens’ genius invention, the cycloidal pendulum.
		The idea is that if a pendulum (bob on a string) is swung between the arches of a cycloid (see demo), then the bob of the pendulum will trace out the involute of a cycloid--a cycloid.
		Since the cycloid is a tautochrone, the pendulum will retain its period even as its amplitude decreases in time.
	www.brown.edu /Students/OHJC/hm4/k.htm (3531 words)

	tautochrone problem
		Find the curve down which an object can slide from any point to the bottom (accelerated by gravity and ignoring friction), always in the same length of time.
		"Tautochrone" comes from the Greek tauto for "the same" (which also gives us "tautology") and chronos for "time." The solution, first found by Christiaan Huygens and published in his Horologium oscillatorium (1673), is a cycloid.
		Thus, if you were to upturn a cycloid, in the manner of an inverted arch, and then release a marble from any point on it, it would take exactly the same time to reach the bottom, no matter where on the curve you started from.
	www.daviddarling.info /encyclopedia/T/tautochrone_problem.html (232 words)

	Tautochrones On Riemannian Manifolds (ResearchIndex)
		The method of fractional calculus is used to study tautochrones on Riemannian manifolds.
		It is mathematically proven that the spring-like physical explanation for tautochrones is the correct one.
		Furthermore, various examples of tautochrones are provided, including one in Euclidean space that demonstrates that the tautochrone problem does not always possess a unique solution.
	citeseer.ist.psu.edu /364273.html (222 words)

	Tautochrone: Definition of Tautochrone in Webster's Dictionary 1913 Edition - Wunder Dictionary (Site not responding. Last check: 2007-11-05)
		Tautochrone: Definition of Tautochrone in Webster's Dictionary 1913 Edition - Wunder Dictionary
		Tautochrone: Definition of Tautochrone in Webster's Dictionary 1913 Edition
		A curved line, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall; as, an inverted cycloid with its base horizontal is a tautochrone.
	websters.wunderdictionary.com /dictionary/def/english/tautochrone.html (68 words)

	Dictionary of Meaning www.mauspfeil.net
		The time is equal to Pi π times the square root of the radius over the gravitation contant.
		The '''tautochrone problem''', the attempt to identify this curve, was solved by Christiaan Huygens Huygens in 1659.
		There you find a list of all editors and the possibility to edit the original text of the article Tautochrone curve.
	www.mauspfeil.net /Tautochrone_curve.html (177 words)

	Weird Words: Tautochrone
		If you position a cycloidal curve like an inverted arch, and release a marble from any point on it, it will always take exactly the same time to reach the bottom, no matter where on the curve you start from.
		So the cycloid is said to be a tautochrone.
		Huygens used this discovery to construct curved jaws from the point of support of the pendulum; these forced its string to follow the right curve no matter how large or small the swing.
	www.worldwidewords.org /weirdwords/ww-tau1.htm (268 words)

	Us and Them (Site not responding. Last check: 2007-11-05)
		tautochrone - this word comes from the Greek tauto, "the same" (which we have inherited in words like tautology) and chronos, "time" (as in chronometer).
		It means a curve of equal time or a curve on which an object falling under gravity will reach the bottom in the same amount of time, no matter from where it starts.
		Seventeenth century Dutch scientist Christaan Huygens discovered that if you position a cycloidal curve like an inverted arch, and release a marble from any point on it, it will always take exactly the same time to reach the bottom, no matter where on the curve you start from.
	www.write101.com /W.Tips288.htm (2117 words)

	Tautochronous: Definition of Tautochronous in Webster's Dictionary 1913 Edition - Wunder Dictionary (Site not responding. Last check: 2007-11-05)
		Tautochronous: Definition of Tautochronous in Webster's Dictionary 1913 Edition - Wunder Dictionary
		Tautochronous: Definition of Tautochronous in Webster's Dictionary 1913 Edition
		Occupying the same time; pertaining to, or having the properties of, a tautochrone.
	websters.wunderdictionary.com /dictionary/def/english/tautochronous.html (34 words)

	Lagrange
		By the end of 1754 he had made some important discoveries on the tautochrone which would contribute substantially to the new subject of the
		Lagrange sent Euler his results on the tautochrone containing his method of maxima and minima.
		His letter was written on 12 August 1755 and Euler replied on 6 September saying how impressed he was with Lagrange's new ideas.
	www-groups.dcs.st-andrews.ac.uk /~history/Mathematicians/Lagrange.html (2914 words)

	Abstract (Site not responding. Last check: 2007-11-05)
		In the tautochrone problem we have a wire higher at one end than the other, and a bead that will slide from the high end to the lowest point.
		We would like to find a shape so that the bead will reach the bottom at identical times no matter where on the wire it started.
		I use Abel's solution as a jumping off point to give a background talk on the fractional calculus, and show why the fractional calculus might be useful in knot theory and dynamical systems.
	www.nmt.edu /~iavramid/seminar/022704abs.html (143 words)

	Tautochrone
		This is the definition of the term Tautochrone
		Tautochrone (n.) A curved line, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall; as, an inverted cycloid with its base horizontal is a tautochrone.
		For people who have trouble spelling, this is the defintion of the term Tautochrone
	linkspider.serversystems.net /dictionary/lookup/tautochrone (108 words)

	TAUTOCHRONE (Site not responding. Last check: 2007-11-05)
		[from Greek expression, for the same time: compare to the French expression tautochrone.].
		The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications.
		Words rhyming with "TAUTOCHRONE" (pronounced '*Tau"tochrone**'): Brachystochrone, Euchrone.
	www.websters-online-dictionary.org /Ta/Tautochrone.html (311 words)

	tautochrone : Definition from the Online Dictionary at Datasegment.com (Site not responding. Last check: 2007-11-05)
		tautochrone : Definition from the Online Dictionary at Datasegment.com
		1 definition found tautochrone - Collaborative International Dictionary of English v.0.48 : Tautochrone *\Tau"tochrone\**, n.
		tautochrone.] (Math.) A curved line, such that a heavy body, descending along it by the action of gravity, will always arrive at the lowest point in the same time, wherever in the curve it may begin to fall; as, an inverted cycloid with its base horizontal is a tautochrone.
	onlinedictionary.datasegment.com /word/Tautochrone (73 words)

	Tautochrone Problem (Site not responding. Last check: 2007-11-05)
		Cycloid satisfies the tautochrone property, consider the derivatives
		Muterspaugh, J.; Driver, T.; and Dick, J. ``The Cycloid and Tautochronism.''
		Muterspaugh, J.; Driver, T.; and Dick, J. ``P221 Tautochrone Problem.''
	www.math.sdu.edu.cn /mathency/math/t/t059.htm (101 words)

	Define Tautochrone : powered by In Dictionary (InDicitonary.com) (Site not responding. Last check: 2007-11-05)
		Define Tautochrone : powered by In Dictionary (InDicitonary.com)
		Use the form below to search our dictionaries by entering a word you wish to define.
		"Tautochrone" gcide "The Collaborative International Dictionary of English v.0.48"
	www.indictionary.com /define/Tautochrone (264 words)

	Medicum Net \| Encyclopedia \| Medical Definitions \| Definition of tautochrone (Site not responding. Last check: 2007-11-05)
		Search the Medicum Encyclopedia Database for definition of tautochrone
		Search the Medicum Books Database for definition of tautochrone
		Search the Medicum Database for definition of tautochrone
	www.medicum.net /dictionary-Medical_Definitions-definition138037-tautochrone.html (137 words)

	Courses (Site not responding. Last check: 2007-11-05)
		(paper on Fractional Derivatives and the Tautochrone Problem)
		Currently, I am working on a paper with Dr. Thomas Osler from Rowan University.
		The paper is entitled "Fractional Derivatives and the Tautochrone Problem." We hope it will be published soon.
	users.rowan.edu /~ruebli62/RowanCourse.htm (58 words)

Tautochrone curve : Tautochrone problem (Site not responding. Last check: 2007-11-05)

Tautochrone curve : Tautochrone problem

Tautochrone curve : Tautochrone problem
article at Free Euro Online Encyclopedia

It uses material from the wikipedia article Tautochrone curve : Tautochrone problem.

www.eurofreehost.com /ta/Tautochrone_problem.html (176 words)

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