A curve connecting two points on which a particle will slide frictionlessly under gravity in the least possible time; the mathematically optimal path between two points.
From Greek brachys 'shortest' plus chronos 'time.' The term was coined by mathematicians in the 17th century to name this famous calculus of variations problem.
The brachistochrone curve isn't a straight line—it's actually a cycloid curve that dips down steeply at first to build up speed, then curves gently up, and this shape beats any other path for fastest descent. It's one of the most beautiful proofs that intuition can fool you.
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