ropelength

In our terms we are asking if there is a knot with ropelength 12.

Such properties include ropelength and various knot energies.

In knot theory each realization of a link or knot has an associated ropelength.

An extensive search has been devoted to showing relations between ropelength and other knot invariants.

This question has been answered, and it was shown to be impossible: the ropelength of any nontrivial knot has to be at least 15.66.

M11: A ropelength of overhanging gymnastic climbing, or up to 15 meters of roof.

As an example there are well known bounds on the asymptotic dependence of ropelength on the crossing number of a knot.

An example of a "physical" invariant is ropelength, which is the amount of 1-inch diameter rope needed to realize a particular knot type.

Knots and links that minimize ropelength are called ideal knots and ideal links respectively.

The thickness τ of a link allows us to introduce a scale with respect to which we can then define the ropelength of a link.

The ropelength of a knot curve C is defined as the ratio , where Len(C) is the length of C and τ(C) is the thickness of the link defined by C.

Ropelength can be turned into a knot invariant by defining the ropelength of a knot type to be the minimum ropelength over all realizations of that knot type.

It has been shown that for each link type there is a ropelength minimizer although it is only of class C. For the simplest nontrivial knot, the trefoil knot, computer simulations have shown that its ropelength is at most 16.372.