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A curve between two points along which a body can move under gravity in a shorter time than for any other curve.
‘Further enhancements will guide the user through the development of brachistochrones for force fields which differ from gravitational force fields.’
‘An inverted cycloid is the brachistochrone, that is the curve between two points in a vertical plane, along which a bead needs the shortest time to travel.’
‘The brachistochrone problem was one of the earliest problems posed in the calculus of variations.’
‘The brachistochrone is a cycloid, but that cycloid is not the only curve satisfying the equation.’
‘Here one can see a graph of the brachistochrone for the given endpoint.’
Origin
Late 18th century: from Greek brakhistos ‘shortest’ + khronos ‘time’.