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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 in 1686, L'Hospital
in 1690, Jakob Bernoulli in 1690, la Hire in 1694, Johann Bernoulli in 1695, Daniel
Bernoulli in 1725, and Euler in 1745 and 1781. An epitrochoid appears in Dürer's
work Instruction in Measurement with Compasses and Straight Edge in 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
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(1)
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(2)
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where 
is the distance from 
to the center of the rolling circle. Special cases include
the limaçon with 
, the circle with 
, and the epicycloid
with 
.
