Bow
Bow
The quartic with implicit equation
| x^4=x^2y-y^3. |
(1)
|
The bow has vertical tangents at (+/-2/9sqrt(3),2/9) and horizontal tangents at (+/-1/4sqrt(2),1/4).
Its curvature is implicitly given by
| kappa(x,y)=(2(-2x^6+3x^4y+48x^6y-60x^4y^2+6x^2y^3+54x^2y^4-9y^5))/((x^4+16x^6-16x^4y-2x^2y^2+9y^4)^(3/2)). |
(2)
|
The area enclosed by the two loops is given by
A = 8/(105)
(3)
= 0.0761904761904...
(4)
(OEIS A118321).
The portion of the curve bounding the two loops has approximate perimeter
| s=1.92151 |
(5)
|
(OEIS A118322).
See also
Knot CurveExplore with Wolfram|Alpha
WolframAlpha
More things to try:
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."Referenced on Wolfram|Alpha
BowCite this as:
Weisstein, Eric W. "Bow." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Bow.html