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Plateau Curves


PlateauCurve

The Plateau curves were studied by the Belgian physicist and mathematician Joseph Plateau. They have Cartesian equation

x=(asin[(m+n)t])/(sin[(m-n)t])
(1)
y=(2asin(mt)sin(nt))/(sin[(m-n)t]),
(2)

where m!=n.

PlateauCurveCircle

If m=2n, the Plateau curves degenerate to

x=a[1+2cos(2nt)]
(3)
y=2asin(2nt),
(4)

which is a circle with center (a,0) and radius 2a.


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References

MacTutor History of Mathematics Archive. "Plateau Curves." http://www-groups.dcs.st-and.ac.uk/~history/Curves/Plateau.html.

Referenced on Wolfram|Alpha

Plateau Curves

Cite this as:

Weisstein, Eric W. "Plateau Curves." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PlateauCurves.html

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