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Dürer Folium


DuererFolium

The Dürer folium is a special case of the rose curve with n=1. It is therefore also an epitrochoid. It has polar equation

 r=asin(theta/2)
(1)

and can be written as a Cartesian equation as

 a^4y^2+4(x^2+y^2)^3=4a^2(x^2+y^2)^2
(2)

or

 (x^2+y^2)[2(x^2+y^2)-a^2]^2=a^4x^2.
(3)

It has arc length

 s=4aE(sqrt(3)i),,
(4)

where E(k) is a complete elliptic integral of the second kind. The area of the outer boundary is given by

 A=1/2a^2(pi+2).
(5)

See also

Epitrochoid, Folium, Rose Curve

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References

Ferréol, R. "Dürer Folium." https://mathcurve.com/courbes2d.gb/foliumdedurer/foliumdedurer.shtml.

Cite this as:

Weisstein, Eric W. "Dürer Folium." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DuererFolium.html

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