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Smooth parametrization of curve $\cosh x+\cosh y = \operatorname{constant}$

Discussion in 'Mathematics' started by Vasily Mitch, Oct 8, 2018.

  1. Vasily Mitch

    Vasily Mitch Guest

    I have a curve (image below) $$ \cosh x+\cosh y = C,\qquad C>2. $$

    I would like to get its smooth parametrization of form $$ x = f(t),\qquad y=g(t),\qquad t\in[a,b], $$ so for every point on the curve there is a corresponding parameter $t$. (In the same manner, as for curve $x^2+y^2=1$, there is a smooth parametrization $x=\cos t$, $y = \sin t$).

    I would appreciate any help. Thanks!

    [​IMG]

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