A Cycloid is a Tautochrone curve, meaning all points take the same time to reach the bottom regardless of initial heightpic.twitter.com/sX94kTPWll
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Any relation to the Brachistochrone curve?
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Is there some transparent reason why the two properties hold? A way to see that a brachistochrone must be tautochronous without computing it?
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I think if there were it wouldn’t have been an open problem for so long and took Newton inventing calculus of variations
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