| 释义 |
NephroidThe 2-Cusped Epicycloid is called a nephroid. Since  ,  , and the equation for  in terms of the parameter  is given by Epicycloid equation
 | (1) |
where
 | (3) |
 | (4) |
The Cartesian equation is
 | (7) |
 and Area  . The Catacaustic forrays originating at the Huygens  showed in 1678that the nephroid is the Catacaustic of a Circle when the light source is at infinity. He published this factin Traité de la luminère in 1690 (MacTutor Archive).See also Astroid, Deltoid, Freeth's Nephroid
References
Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 169-173, 1972.Lee, X. ``Nephroid.''http://www.best.com/~xah/SpecialPlaneCurves_dir/Nephroid_dir/nephroid.html. Lockwood, E. H. ``The Nephroid.'' Ch. 7 in A Book of Curves. Cambridge, England: Cambridge University Press, pp. 62-71, 1967. MacTutor History of Mathematics Archive. ``Nephroid.''http://www-groups.dcs.st-and.ac.uk/~history/Curves/Nephroid.html. Yates, R. C. ``Nephroid.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 152-154, 1952. |
