The path traced out by a fixed point at a radius , where is the radius of a rolling circle ,
also sometimes called an extended cycloid. The prolate cycloid contains loops, and
has parametric equations
The arc length from is
(3)
where
(4)
(5)
See also Curtate Cycloid ,
Cycloid ,
Prolate Cycloid Evolute ,
Trochoid
Explore with Wolfram|Alpha
References Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 216,
1987. Harris, J. W. and Stocker, H. Handbook
of Mathematics and Computational Science. New York: Springer-Verlag, p. 325,
1998. Lawrence, J. D. A
Catalog of Special Plane Curves. New York: Dover, pp. 192 and 194-197,
1972. Lockwood, E. H. A
Book of Curves. Cambridge, England: Cambridge University Press, p. 146,
1967. Steinhaus, H. Mathematical
Snapshots, 3rd ed. New York: Dover, pp. 147-148, 1999. Zwillinger,
D. (Ed.). CRC
Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, p. 292,
1995. Referenced on Wolfram|Alpha Prolate Cycloid
Cite this as:
Weisstein, Eric W. "Prolate Cycloid."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/ProlateCycloid.html
Subject classifications