Editing Tautochrone curve (section)

{{short description|Curve for which the time to roll to the end is equal for all starting points}}
[[File:Tautochrone curve.gif|300px|right|thumb|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.]]
[[File:Objects representing tautochrone curve 03.gif|thumb|300px|Objects representing tautochrone curve]]

A '''tautochrone curve''' or '''isochrone curve''' ({{ety|grc|''ταὐτό'' ([[wikt:tauto-|tauto-]])|same||''ἴσος'' ([[wikt:iso-|isos-]])|equal||''χρόνος'' ([[wikt:chrono-#English|chronos]])|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 on the curve.  The curve is a [[cycloid]], and the time is equal to [[Pi|π]] times the [[square root]] of the radius of the circle which generates the cycloid, over the [[Gravitational acceleration|acceleration of gravity]].  The tautochrone curve is related to the [[brachistochrone curve]], which is also a cycloid.