DPLL algorithm

Rotated Quadrifolium

The quadrifolium (also known as four-leaved clover^[1]) is a type of rose curve with n=2. It has polar equation:

r = \cos (2 θ),

with corresponding algebraic equation

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

Rotated by 45°, this becomes

r = \sin (2 θ)

with corresponding algebraic equation

(x^{2} + y^{2})^{3} = 4 x^{2} y^{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} + 108 x^{2} y^{2} = 16 (x^{2} + 7 y^{2}) (y^{2} + 7 x^{2}) (x^{2} + y^{2}) + 729 (x^{2} + y^{2}) .

File:Dualrose.png

Dual Quadrifolium

The area inside the curve is $\frac{1}{2} π$ , which is exactly half of the area of the circumcircle of the quadrifolium. The length of the curve is ca. 9.6884.^[2]

Notes

↑ C G Gibson, Elementary Geometry of Algebraic Curves, An Undergraduate Introduction, Cambridge University Press, Cambridge, 2001, ISBN 978-0-521-64641-3. Pages 92 and 93
↑ Quadrifolium - from Wolfram MathWorld

References

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External links

Interactive example with JSXGraph

[1] C G Gibson, Elementary Geometry of Algebraic Curves, An Undergraduate Introduction, Cambridge University Press, Cambridge, 2001, ISBN 978-0-521-64641-3. Pages 92 and 93

[2] Quadrifolium - from Wolfram MathWorld

[1]

[2]

DPLL algorithm

Notes

References

External links

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