brachistochrone

[bruh-kis-tuh-krohn]

noun

Mechanics.

1. the curve between two points that in the shortest time by a body moving under an external force without friction; the curve of quickest descent.

brachistochrone

/ brəˈkɪstəˌkrəʊn /

noun

1. maths the curve between two points through which a body moves under the force of gravity in a shorter time than for any other curve; the path of quickest descent

Other Word Forms

• brachistochronic adjective
• brachistochronous adjective

Word History and Origins

Origin of brachistochrone¹

1765–75; < Greek bráchisto ( s ) shortest (superlative of brachýs brachy- ) + chrónos time

Word History and Origins

Origin of brachistochrone¹

C18: from Greek brakhistos , superlative of brakhus short + chronos time

Example Sentences

Galileo discovered it was the brachistochrone curve, which, despite being longer, delivers the ball first.

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One exhibit in particular caught my eye: a marble run with two paths of descent, the first a straight decline and the other a longer, lazy bend called the brachistochrone curve that goes down and then up again.

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In 1696, the Swiss mathematician Johann Bernoulli challenged his colleagues to solve an unresolved issue called the brachistochrone problem, specifying the curve connecting two points displaced from each other laterally, along which a body, acted upon only by gravity, would fall in the shortest time.

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Before leaving for work the next morning, he had invented an entire new branch of mathematics called the calculus of variations, used it to solve the brachistochrone problem and sent off the solution, which was published, at Newton’s request, anonymously.

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To understand the true relation of these theories in that part of the field where they seem equally applicable we must look at them in the light which Hamilton has thrown upon them by his discovery that to every brachistochrone problem there corresponds a problem of free motion, involving different velocities and times, but resulting in the same geometrical path.

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