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Links Curve

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LinksCurve

The links curve is the quartic curve given by the Cartesian equation

(x^2+y^2-3x)^2=4x^2(2-x).
(1)

The area enclosed by the outer envelope is

A_(envelope)=1/6(9pi+8)
(2)

and the area of the inner loop is

A_(inner loop)=1/6(3pi-8).
(3)

The origin of the curve is a tacnode.

See also

Bifolium, Capricornoid, Tacnode

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References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 72, 1989.

Cite this as:

Weisstein, Eric W. "Links Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LinksCurve.html

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