Cruciform
Cruciform
A plane quartic curve also called the cross curve or policeman on point duty curve (Cundy and Rollett 1989). It is given by the implicit equation
| x^2y^2-b^2x^2-a^2y^2=0, |
(1)
|
which is equivalent to
and
| [画像: y^2=(b^2x^2)/(x^2-a^2). ] |
(3)
|
In parametric form,
x = asect
(4)
y = bcsct.
(5)
The curvature is given by
which, in the special case a=b, reduces to
![画像: kappa=(48sqrt(2)cos^4tsin^4t)/(a[5+3cos(4t)]^(3/2)).](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/Cruciform/NumberedEquation4.svg){kind=link}
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References
Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 71, 1989.Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 127 and 130-131, 1972.Referenced on Wolfram|Alpha
CruciformCite this as:
Weisstein, Eric W. "Cruciform." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Cruciform.html