Quadrifolium

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

r = acos(2θ),

with corresponding algebraic equation

(x^{2} + y^{2})^{3} = a2(x^{2} − y^{2})^{2}

Rotated by 45°, this becomes

r = asin(2θ)

with corresponding algebraic equation

(x^{2} + y^{2})^{3} = 4ax^{2}y^{2} .

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

Undergraduate Texts in Mathematics

Graduate Studies in Mathematics

Retrieved from "http://en.wikipedia.org/"

All text is available under the terms of the GNU Free Documentation License