A curve between two points along which a body can move under gravity in a shorter time than for any other curve.
- 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.
- Further enhancements will guide the user through the development of brachistochrones for force fields which differ from gravitational force fields.
Late 18th century: from Greek brakhistos 'shortest' + khronos 'time'.
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