brachistochrone

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DFW's Sentence The closest conventional analogue I could derive for this figure was a cycloid, L'Hopital's solution to Bernoulli's famous brachistochrone problem, the curve traced by a fixed point on the circumference of a circle rolling along a straight line.

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  1. The curve upon which a body moves in the least possible time from one given point to another. According to the nature of the forces that are supposed to act upon the body, and the constraints to which it may be subject, the brachistochrone takes various geometrical forms, mostly spiral or consisting of branches united by cusps, like the cycloid, which is the brachistochrone for a body moving under a constant force and subject to no condition except that defining the brachistochrone. Until recently always spelled brachystochrone.

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Examples (3)

  • DFW's Sentence The closest conventional analogue I could derive for this figure was a cycloid, L'Hopital's solution to Bernoulli's famous brachistochrone problem, the curve traced by a fixed point on the circumference of a circle rolling along a straight line. —  Griffin And Hoxie Mega Feed
  • My Sentence Shelby Donald stood among the remains of last night's argument, the third in as many days, when she realized she was caught in a brachistochrone problem of no small significant for no matter how loudly she availed upon the God's of better judgement her inbreed intemperance demanded satisfaction and would always gravitate her towards the most mercurial of men. —  Griffin And Hoxie Mega Feed
  • 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. —  Five of Maxwell's Papers
 

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Etymologies (1)

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  1. Word invented by John Bernoulli in 1694; from Greek βράχιστος, superlative of βραχύς, short, + χρόυος, time: see chronic.
 

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