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
Cite this as:
Weisstein, Eric W. "Prolate Cycloid." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ProlateCycloid.html