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
| [画像: r=asin(theta/2) ] |
(1)
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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)
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or
| (x^2+y^2)[2(x^2+y^2)-a^2]^2=a^4x^2. |
(3)
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It has arc length
| s=4aE(sqrt(3)i),, |
(4)
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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 CurveExplore with Wolfram|Alpha
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References
Ferréol, R. "Dürer Folium." https://mathcurve.com/courbes2d.gb/foliumdedurer/foliumdedurer.shtml.Referenced on Wolfram|Alpha
Dürer FoliumCite this as:
Weisstein, Eric W. "Dürer Folium." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DuererFolium.html