National Science Foundation
National Curve Bank

Brachistochrone ~ Cycloid

Deposit #88

Al Lehnen


A Comparison of Times of Fastest Descent

This section . . . .

Brachistochrone-cycloid animation

The Brachistochrone-Cycloid Revisited:  A Timely Consideration
 
Brachistochrone Equations

( Please open the "pdf" file for the continuing text and graphs.)


Text
 Graph of descent times


References
For Lehnan's description of Deposit # 88 . . .
 		MAA button
Lehnan presented his work
at MathFest 2008.
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, 192-197, 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. 167-171.
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, 206-208, 1996.