Plateau Curves
PlateauCurve
The Plateau curves were studied by the Belgian physicist and mathematician Joseph Plateau. They have Cartesian equation
x = [画像:(asin[(m+n)t])/(sin[(m-n)t])]
![画像:(asin[(m+n)t])/(sin[(m-n)t])](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/PlateauCurves/Inline3.svg){kind=link}
(1)
y = [画像:(2asin(mt)sin(nt))/(sin[(m-n)t]),]
![画像:(2asin(mt)sin(nt))/(sin[(m-n)t]),](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/PlateauCurves/Inline6.svg){kind=link}
(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." https://mathshistory.st-andrews.ac.uk/Curves/Plateau/.Referenced on Wolfram|Alpha
Plateau CurvesCite this as:
Weisstein, Eric W. "Plateau Curves." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PlateauCurves.html