The dumbbell curve is the sextic curve
(1)
|
It has area
(2)
|
and approximate arc length
(3)
|
For the parametrization
(4)
| |||
(5)
|
the curvature is
(6)
|
The dumbbell curve is the sextic curve
(1)
|
It has area
(2)
|
and approximate arc length
(3)
|
For the parametrization
(4)
| |||
(5)
|
the curvature is
(6)
|
Weisstein, Eric W. "Dumbbell Curve." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DumbbellCurve.html