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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
.
