A certified upper bound for the distortion of the trefoil knot
The distortion of a rectifiable closed curve $\gamma\subset\mathbb R^3$ is the supremum, over pairs of distinct points, of the ratio of the length of the shorter arc of $\gamma$ between them to their distance; the distortion $\delta(K)$ of a knot type $K$ is the infimum over all curves of type $K$. For the trefoil, the published lower bound is $\delta\ge5\pi/3$, valid for every non-trivial knot (a recent preprint claims $\delta>6.5321$), and the only upper bound we found in the literature is the value $7.16$ obtained by numerical simulation. We exhibit an explicit polygon with $192$…
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