Colorado Education Initiative

An improved lower bound for the distortion of a knotted curve

We prove that every non-trivial rectifiable tame knot embedding K ⊂ R³ has distortion δ(K) > 6.5321. Consequently, the infimum within every non-trivial tame knot type is at least 6.5321. This improves the 6.32 bound in version 1.0 by 0.2121. The proof combines essential-secant pr...