= Logarithmic conical helix
{title2=$x(s)=(\tfrac s2\cos\log s,\tfrac s2\sin\log s,s/\sqrt2)$}
The displayed <space curve>, $s>0$, lies on a cone and is parametrized by <arc length>. It has a constant tangent angle with its axis, while the turn spacing shrinks geometrically toward the limiting apex. Its <curvature> is $1/(\sqrt2s)$: differentiate its unit tangent with respect to $s$. Infinitely many turns accumulate at the apex with finite <arc length>; the apex itself is not a regular point of the curve.
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