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brachistochrone


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cycloid

Isaac Newton (1642—1727) natural philosopher and mathematician

Gottfried Wilhelm Leibniz (1646—1716) German rationalist philosopher, mathematician, and logician

 

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Suppose that A and B are points in a vertical plane, where B is lower than A but not vertically below A. Imagine a particle starting from rest at A and travelling along a curve from A to B under the force of gravity. The curve with the property that the particle reaches B as soon as possible is called the brachistochrone (from the Greek for ‘shortest time’). The straight line from A to B does not give the shortest time. The required curve is a cycloid, vertical at A and horizontal at B. The problem was posed in 1696 by Jean * Bernoulli and his solution, together with others by * Newton, * Leibniz and Jacques Bernoulli, was published the following year.

Subjects: Mathematics.


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