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/bɹəˈkɪstəkɹəʊn/ · noun
(mathematics) A cycloid; the curve of fastest descent between two points..
Let A and B be two fixed points. Then the time it takes a particle to slide under the influence of gravity along some path joining A and 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 A to B is called the brachistochrone.
Use brachistochrone when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Brachistochrone means (mathematics) A cycloid; the curve of fastest descent between two points..
The closest synonym depends on the sentence and intended sense.
The opposite depends on the specific sense.
Let A and B be two fixed points. Then the time it takes a particle to slide under the influence of gravity along some path joining A and 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 A to B is called the brachistochrone.
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