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Keratoid Cusp

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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

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 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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