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Bow

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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 Curve

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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."

Cite this as:

Weisstein, Eric W. "Bow." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Bow.html

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