brachistochrone

From Ancient Greek βράχιστος (brákhistos, “shortest”) + χρόνος (khrónos, “time”). The term was coined by Johann Bernoulli.^[1]

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brachistochrone

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brachistochrone (plural brachistochrones)

1. (mathematics) A cycloid; the curve of fastest descent between two points.
   • 1963, Gelfand, I.M. and S.V. Fomin, Calculus of Variations, Prentice-Hall, Inc., page 3:

     Let ${\displaystyle A}$ and ${\displaystyle B}$ be two fixed points. Then the time it takes a particle to slide under the influence of gravity along some path joining ${\displaystyle A}$ and ${\displaystyle B}$ depends on the choice of the path (curve), and hence is a functional. The curve such that the particle takes the least time to go from ${\displaystyle A}$ to ${\displaystyle B}$ is called the brachistochrone.