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Rose curve with angular frequency 2
This article is about the geometric shape. For the plant, see
Four-leaf clover. For the symmetrical shape framework, see
Quatrefoil.
The quadrifolium (also known as four-leaved cloverpolar equation
:
with corresponding algebraic equation
Rotated counter-clockwise by 45°, this becomes
with corresponding algebraic equation
In either form, it is a plane algebraic curve of genus zero.
The dual curve to the quadrifolium is
The area inside the quadrifolium is , which is exactly half of the area of the circumcircle of the quadrifolium. The perimeter of the quadrifolium is
where is the complete elliptic integral of the second kind with modulus , is the arithmetic–geometric mean and denotes the derivative with respect to the second variable.[2]
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