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In 1696 Bernoulli posed the Brachistochrone problem, challenging other mathematicians to attempt to solve it. 


Bernoulli solved the problem by using a property of optics and found that the Brachistochrone is the path of a Cycloid.






a path between two points along which a body can move under gravity in a shorter time than for any other path.

Given two points A and B in a vertical plane, what is the path traced out by a point acted on only by gravity which starts at A and reaches B in the shortest time? 

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