Tautochrone curve

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Tautochrone curve

►From Wikipedia:
[In Mathematics] A tautochrone or isochrone curve (from Greek prefixes tauto- meaning same or iso- equal, and chrono time) is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point.

The curve is a cycloid, and the time is equal to π times the square root of the radius over the acceleration of gravity. The tautochrone curve is the same as the brachistochrone curve for any given starting point.

Read more>> http://en.wikipedia.org/wiki/Tautochrone_curve

Animation explanation:
Four balls slide down a cycloid curve from different positions, but they arrive at the bottom at the same time. The blue arrows show the points’ acceleration along the curve. On the top is the time-position diagram.

Animation source>>
http://en.wikipedia.org/wiki/Tautochrone_curve#mediaviewer/File:Tautochrone_curve.gif

Credit:
Claudio Rocchini rewritten by Geek3 – Own work

Further reading

Cycloid>> http://en.wikipedia.org/wiki/Cycloid

Brachistochrone curve>>
http://en.wikipedia.org/wiki/Brachistochrone_curve

Tautochrone Problem on MathWorld >>
http://mathworld.wolfram.com/TautochroneProblem.html

#mathematics #cycloid #Tautochrone_curve

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