Maltese Cross Curve
MalteseCrossCurve
The Maltese cross curve is the quartic algebraic curve with Cartesian equation
| xy(x^2-y^2)=x^2+y^2 |
(1)
|
and polar equation
| [画像: r=2/(sqrt(sin(4theta))) ] |
(2)
|
(Cundy and Rollett 1989, p. 71), so named for the curve's resemblance to the Maltese cross.
It has curvature and tangential angle given by
kappa(t) = [画像:sqrt(2)[3cos(8t)-11][(sin(4t))/(5+3cos(8t))]^(3/2)]
![画像:sqrt(2)[3cos(8t)-11][(sin(4t))/(5+3cos(8t))]^(3/2)](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/MalteseCrossCurve/Inline3.svg){kind=link}
(3)
phi(t) = -cot^(-1)[2cot(4t)].
(4)
See also
Maltese CrossExplore with Wolfram|Alpha
WolframAlpha
References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 71, 1989.Referenced on Wolfram|Alpha
Maltese Cross CurveCite this as:
Weisstein, Eric W. "Maltese Cross Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MalteseCrossCurve.html