Dumbbell Curve

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DumbbellCurve

The dumbbell curve is the sextic curve

a^4y^2=x^4(a^2-x^2).

(1)

It has area

A=1/4pia^2

(2)

and approximate arc length

s approx 5.541a.

(3)

For the parametrization

x = at

(4)

y = at^2sqrt(1-t^2),

(5)

the curvature is

[画像: kappa=(2-9t^2+6t^4)/(a(1+3t^2-12t^4+9t^6)^(3/2)). ]

(6)

See also

Barbell Graph, Butterfly Curve, Devil's Curve, Eight Curve, Lemniscate, Piriform Curve, Teardrop Curve

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References

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

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Cite this as:

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

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