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Bicuspid Curve


BicuspidCurve

The quartic curve given by the implicit equation

 (x^2-a^2)(x-a)^2+(y^2-a^2)^2=0,
(1)

so-named because of its resemblance to a tooth.

The bicuspid curve has cusps at (a,-a) and (a,a).

The horizontal tangents are located at (-1/2,+/-sqrt(1+3/4sqrt(3))), and the vertical tangents at (-1,+/-1), (0,0), and ((x^3-2x^2+2)_1,0), where (P(x))_n is a polynomial root.

The bicuspid with a=1 has approximate area

 A approx 3.74661
(2)

and approximate perimeter

 s=9.86177.
(3)

See also

Bean Curve, Stirrup Curve, Tooth Surface

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References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 73, 1989.

Cite this as:

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

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