The bow is the quartic curve with implicit equation
 |
(1)
|
It has parametric equations 
and 
,
where 
is a real
number. The intervals 
and 
trace the two loops. The
bow has vertical tangents at 
and horizontal tangents
at 
.
At points where 
,
its signed curvature for the orientation with unit
tangent vector 
is given by
 |
(2)
|
where 
and 
and 
denote its partial derivatives. The origin
is the only point of the curve where both partial
derivatives vanish, so this implicit curvature
formula applies when 
.
The area enclosed by the two loops is given by
 |  |  |
(3)
|
 |  |  |
(4)
|
(OEIS A118321).
The portion of the curve bounding the two loops has approximate perimeter
 |
(5)
|
(OEIS A118322).
