= Tractrix
{title2=$r=\sin\theta,\quad h=\cos\theta+\log\tan(\theta/2)$}
{wiki}
A <tractrix> is a <plane curve> whose tangent segment from the point of contact to a fixed axis has constant length. For segment length one and a positive acute tangent angle $\theta$, its height is $r=\sin\theta$. The slope relation $dr/dh=\tan\theta$ gives $dh/d\theta=\cos^2\theta/\sin\theta$. Integrating yields the displayed axial coordinate up to an additive constant. Conversely these coordinates have the required slope, and their tangent intercept is at distance $r/\sin\theta=1$. Rotating this profile about its axis gives a <tractoid>.
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