Epitrochoid
 |  |
 |  |
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
 |  |  |
(1)
|
 |  |  |
(2)
|
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 
.
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epitrochoid
