Hypotrochoid
 |
The Roulette traced by a point 
attached to a Circle of radius 
rolling around the inside of a fixed Circle of radius 
. The parametric equations for a hypotrochoid are
 |  |  | (1) |
 | |  | (2) |
where
and 
is the distance from to the center of the rolling Circle. Special cases includethe Hypocycloid with 
, the Ellipse with 
, and the Rose with | |  | (3) |
 | |  | (4) |
See also Epitrochoid, Hypocycloid, Spirograph
References
Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 165-168, 1972. Lee, X. ``Hypotrochoid.''http://www.best.com/~xah/SpecialPlaneCurves_dir/Hypotrochoid_dir/hypotrochoid.html Lee, X. ``Epitrochoid and Hypotrochoid Movie Gallery.''http://www.best.com/~xah/SpecialPlaneCurves_dir/EpiHypoTMovieGallery_dir/epiHypoTMovieGallery.html MacTutor History of Mathematics Archive. ``Hypotrochoid.''http://www-groups.dcs.st-and.ac.uk/~history/Curves/Hypotrochoid.html.
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