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The curve along which a smooth-sliding particle, under the influence of gravity alone, will fall from one point to another in the minimum time.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.



the curve of most rapid descent—that is, the one of all possible curves connecting two given points A and B of a potential force field that a mass point moving along the curve with an initial velocity equal to zero and acted upon only by the forces of the field will traverse from position A to position B in the shortest time. When the movement occurs in a homogeneous gravitational field, the brachistochrone is a cycloid with a horizontal base and a point of return that coincides with point A. The solution of the brachistochrone problem (Johann Bernoulli, 1696) served as the starting point for the development of the calculus of variations. The error of Galileo, who tried to prove that the brachistochrone is a circumferential arc, is instructive. (See G. Galilei, Izbrannye trudy, vol. 2, Moscow, 1964, pp. 298-301, note 465.)

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.