Wrapped hyperbolic cosine curve
= Wrapped hyperbolic cosine curve
{title2=$\mathbf r(t)=(\cos t,\sin t,\cosh t)$}
For $-\pi\leq t\leq\pi$, this <parametric curve> closes with a corner on a unit <circular cylinder>. Its <speed> is $\cosh t$, so its <arc length> is $2\sinh\pi$. The <cylindrical surface> between the <curve> and $z=0$ has the same <surface area>, because unrolling gives the <integral> $\int_{-\pi}^{\pi}\cosh t\,dt$.