The quartic with implicit equation
 |
(1)
|
The bow has vertical tangents at 
and horizontal tangents at 
.
Its curvature is implicitly given by
 |
(2)
|
The area enclosed by the two loops is given by
 |
 |
 |
(3)
|
 |
 |
 |
(4)
|
(Sloane's A118321).
The portion of the curve bounding the two loops has approximate perimeter
 |
(5)
|
(Sloane's A118322).
SEE ALSO:Knot Curve
REFERENCES:
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 72, 1989.
Sloane, N. J. A. Sequences A118321 and A118322 in "The On-Line Encyclopedia of Integer Sequences."
