A "Cycloid" curve is one for which all objects take the 𝑠𝑎𝑚𝑒 amount of time to reach the bottom • If this seems counterintuitive, remember that 𝑚𝑔ℎ=½𝑚𝑣², and so objects starting higher will have a larger final velocitypic.twitter.com/EV4ZzT6YFo
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A Cycloid curve is also called a "Tautochrone" (meaning equal time) Mathematically, the Brachistochrone and the Cycloid are the same curve, but they arise from slightly different but related problems (equal time & least time) Brachistochrone ⇔ Cycloid Tautochrone ⇔ Cycloid
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We learn in high school that the "period of a pendulum is independent of its amplitude"--i.e that it's isochronus. • This isn't quite true; it's only true for *small* angles θ • In reality, a pendulum's period is only independent of its amplitude if it moves along a cycloidpic.twitter.com/d1Vh1VlJ9u
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gif credits: Brachistochrone: Robert Ferréol (Wikipedia) Tautochrone: Claudio Rocchini (Wikipedia) Pendulum : Rem088roy (Wikipedia)
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A Cycloid is the curve traced out by a point on a rolling wheelpic.twitter.com/3BgmeSPDQF
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gif credit: Cycloid rolling (last gif): IchibanPL (Wikipedia)
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sick viz bra
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The Brachistochrone curve is also the Tautochrone curve: any body positioned in any different points in the curve, and affected only by local gravity, hits its end in the same time. (animation from Wikipedia, heheh)pic.twitter.com/1BWBhbvaJz
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Yes! I was adding that to the thread when you posted!
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| Maths Moonlighter