Definitions
Nearby Words

The quadrifolium is a type of rose curve with n=2. It has polar equation:

$r = cos\left(2theta\right) ,$,

with corresponding algebraic equation

$\left(x^2+y^2\right)^3 = \left(x^2-y^2\right)^2 ,$.

Rotated by 45°, this becomes

$r = sin\left(2theta\right) ,$

with corresponding algebraic equation

$\left(x^2+y^2\right)^3 = 4x^2y^2 ,$.

In either form, it is a plane algebraic curve of genus zero.

The dual curve to the quadrifolium is

$\left(x^2-y^2\right)^4 + 837\left(x^2+y^2\right)^2 + 108x^2y^2 = 16\left(x^2+7y^2\right)\left(y^2+7x^2\right)\left(x^2+y^2\right)+729\left(x^2+y^2\right) ,$.

## References

Search another word or see Quadrifoliumon Dictionary | Thesaurus |Spanish