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The Brachistochrone problem... A classic example of the calculus of variations is to find the brachistochrone, defined as that smooth curve joining two points A and B (not underneath one another) along which a particle will slide from A to B under gravity in the fastest possible time. The path of the quickest descent is not a straight line but a brachistochrone curve. Johann Bernoulli investigated the Brachistochrone problem and offered a challenge, specifically aimed at his older Brother Jacob
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The Brachistocrone problem, which seeks the curve of quickest descent for a particle under gravity, was famously posed by Johann Bernoulli in 1696. The solution, a cycloid, was found by several mathematicians, including Newton, who solved it in a single night, and the Bernoulli brothers. Galileo had previously studied a related problem but incorrectly concluded the optimal curve was an arc of a circle. | Mathematics Learning
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