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 SurfaceExplore with Wolfram|Alpha
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References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 73, 1989.Referenced on Wolfram|Alpha
Bicuspid CurveCite this as:
Weisstein, Eric W. "Bicuspid Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BicuspidCurve.html