
Brachistochrone
~ Cycloid
A Comparison of Times of Fastest Descent
The
BrachistochroneCycloid Revisited: A Timely Consideration
( Please open the "pdf" file
for the continuing text and graphs.)

References


Carr, George S., Formulas
and Theorems in PURE MATHEMATICS, 2nd ed., Chelsea Publishing
Co., New
York, 1970. Reprint of Carr's 1886 edition under the title of A
Synopsis of Elementary Results in Pure
Mathematics, London and
Cambridge.

N. P. Johnson,"The
Brachistochrone Problem", The
College Mathematics Journal 35, 192197, 2004.

W. S. Kimball,
Calculus of Variations, Butterworths Scientific Publications, London,
1952, p. 328.

Gray, Alfred, Modern Differential Geometry of Curves and Surfaces with MATHEMATICA^{®}, CRC Press, 1998, p. 1027. 
Lockwood, E. H., A Book of Plane Curves, Campridge University Press, 1961, pp. 167171. 
Weisstein, E. W., CRC Concise Encyclopedia of Mathematics, CRC Press, 1999, pp. 589  590. See Evolute. 
J. Zeng, "A Note on
the Brachistochrone Problem", The
College Mathematics Journal 27, 206208, 1996.

The
National Curve Bank
thanks Al Lehnen for Deposit #88. < alehnen@matcmadison.edu
>
The NCB also thanks the Istituto
e Museo
di Storia della Scienza of Florence, Italy and the Huntington
Library
of San Marino, California for permission to use the illustrations.


