The Dürer folium is a special case of the rose curve with 
.
It is therefore also an epitrochoid. It has polar
equation
 |
(1)
|
and can be written as a Cartesian equation as
 |
(2)
|
or
![(x^2+y^2)[2(x^2+y^2)-a^2]^2=a^4x^2.](/images/equations/DuererFolium/NumberedEquation3.svg) |
(3)
|
It has arc length
 |
(4)
|
where 
is a complete elliptic integral
of the second kind. The area of the outer boundary is given by
 |
(5)
|
