  The distortion of a curve measures the maximum arc/chord length ratio. Gromov
showed any closed curve has distortion at least pi/2 and asked about the
distortion of knots. Here, we prove that any nontrivial tame knot has
distortion at least 5pi/3; examples show that distortion under 7.16 suffices to
build a trefoil knot. Our argument uses the existence of a shortest essential
secant and a characterization of borderline-essential arcs.
