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
 |
(1)
|
which is equivalent to
 |
(2)
|
and
 |
(3)
|
In parametric form,
The curvature is given by
which, in the special case
,
reduces to
![kappa=(48sqrt(2)cos^4tsin^4t)/(a[5+3cos(4t)]^(3/2)).](/images/equations/Cruciform/NumberedEquation4.svg) |
(8)
|
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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
Cruciform
Cite this as:
Weisstein, Eric W. "Cruciform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Cruciform.html
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