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Maltese Cross Curve

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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

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)=sqrt(2)[3cos(8t)-11][(sin(4t))/(5+3cos(8t))]^(3/2)
(3)
phi(t)=-cot^(-1)[2cot(4t)].
(4)

See also

Maltese Cross

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References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 71, 1989.

Cite this as:

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

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