Keratoid Cusp
KeratoidCusp
The keratoid cusp is quintic algebraic curve defined by
| y^2=x^2y+x^5. |
(1)
|
It has a ramphoid cusp at the origin, horizontal tangents at (0,0) and (-6/(25),(108)/(3125)), and a vertical tangent at (-1/4,1/(32)).
The curvature is given implicitly by
| [画像: kappa(x,y) =(2(25x^8+3x^4y+40x^5y-40x^3y^2-4y^3))/((x^4+25x^8-4x^2y+20x^5y+4y^2+4x^2y^2)^(3/2)). ] |
(2)
|
The loop has area
| A=1/(420) |
(3)
|
and arc length
| s approx 0.510095. |
(4)
|
See also
Ramphoid CuspExplore with Wolfram|Alpha
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References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 72, 1989.Referenced on Wolfram|Alpha
Keratoid CuspCite this as:
Weisstein, Eric W. "Keratoid Cusp." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/KeratoidCusp.html