
The Roulette traced by a point attached to a Circle of radius rolling around the outside of a fixed Circle of radius . These curves were studied by Dürer (1525), Desargues (1640), Huygens (1679), Leibniz, Newton (1686), L'Hospital (1690), Jakob Bernoulli (1690), la Hire (1694), Johann Bernoulli (1695), Daniel Bernoulli (1725), Euler (1745, 1781). An epitrochoid appears in Dürer's work Instruction in Measurement with Compasses and Straight Edge (1525). He called epitrochoids Spider Lines because the lines he used to construct the curves looked like a spider.
The parametric equations for an epitrochoid are
See also Epicycloid, Hypotrochoid, Spirograph, Trochoid
References
Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 168170, 1972.
Lee, X. ``Epitrochoid.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/Epitrochoid_dir/epitrochoid.html.
Lee, X. ``Epitrochoid and Hypotrochoid Movie Gallery.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/EpiHypoTMovieGallery_dir/epiHypoTMovieGallery.html.