Trefoil Curve
TrefoilCurve
The "trefoil" curve is the name given by Cundy and Rollett (1989, p. 72) to the quartic plane curve given by the equation
| x^4+x^2y^2+y^4=x(x^2-y^2). |
(1)
|
As such, it is a simply a modification of Kepler's folium with a=1 and b=2
| x^4+2x^2y^2+y^4=2x(x^2-y^2) |
(2)
|
obtained by dropping the coefficients 2.
The area enclosed by the trefoil curve is
| [画像: A=(a^2pi)/(4sqrt(3)), ] |
(3)
|
the geometric centroid (x^_,y^_) of the enclosed region is
x^_ = 1/2a
(4)
y^_ =
(5)
and the area moment of inertia elements by
(E. Weisstein, Feb 3, 2018).
See also
Fish Curve, Kepler's Folium, Talbot's Curve, Trefoil Knot, TrifoliumExplore 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
Trefoil CurveCite this as:
Weisstein, Eric W. "Trefoil Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrefoilCurve.html