Relationship To The Trisectrix of MacLaurin
The folium of Descartes is related to the trisectrix of Maclaurin by affine transformation. To see this, start with the equation
- ,
and change variables to find the equation in a coordinate system rotated 45 degrees. This amounts to setting . In the plane the equation is
- .
If we stretch the curve in the direction by a factor of this becomes
which is the equation of the trisectrix of Maclaurin.
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