Brachistochrone curve. Fastest route for ball.

"A Brachistochrone curve is the fastest path
for a ball to roll between two points that are at
different heights. A ball can roll along the curve
faster than a straight line between the points.
The curve will always be the quickest route
regardless of how strong gravity is or how
heavy the object is. However, it might not be
the quickest if there is friction.
The curve can be found using calculus of
variations and optimal control."

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