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Rose curve with angular frequency 2 From Wikipedia, the free encyclopedia
The quadrifolium (also known as four-leaved clover[1]) is a type of rose curve with an angular frequency of 2. It has the polar 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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