- Quadrifolium
The quadrifolium is a type of rose curve with n=2. It has
polar equation ::r = cos(2 heta) ,,
with corresponding algebraic equation
:x^2+y^2)^3 = (x^2-y^2)^2 ,.
Rotated by 45°, this becomes
:r = sin(2 heta) ,
with corresponding algebraic equation
:x^2+y^2)^3 = 4x^2y^2 ,.
In either form, it is a plane algebraic curve of genus zero.
The dual curve to the quadrifolium is
:x^2-y^2)^4 + 837(x^2+y^2)^2 + 108x^2y^2 = 16(x^2+7y^2)(y^2+7x^2)(x^2+y^2)+729(x^2+y^2) ,.
References
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