
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) 
(3)  
(4) 
See also Epitrochoid, Hypocycloid, Spirograph
References
Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 165168, 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://wwwgroups.dcs.stand.ac.uk/~history/Curves/Hypotrochoid.html.