The keratoid cusp is quintic algebraic
curve defined by
![y^2=x^2y+x^5.](/images/equations/KeratoidCusp/NumberedEquation1.svg) |
(1)
|
It has a ramphoid cusp at the origin, horizontal tangents at
and
, and a vertical
tangent at
.
The curvature is given implicitly by
![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)).](/images/equations/KeratoidCusp/NumberedEquation2.svg) |
(2)
|
The loop has area
![A=1/(420)](/images/equations/KeratoidCusp/NumberedEquation3.svg) |
(3)
|
and arc length
![s approx 0.510095.](/images/equations/KeratoidCusp/NumberedEquation4.svg) |
(4)
|
See also
Ramphoid Cusp
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References
Cundy, H. and Rollett, A. Mathematical
Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 72, 1989.
Cite this as:
Weisstein, Eric W. "Keratoid Cusp." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KeratoidCusp.html
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