Ropelength

In physical knot theory, each realization of a link or knot has an associated ropelength. Intuitively this is the minimal length of an ideally flexible rope that is needed to tie a given link, or knot. Knots and links that minimize ropelength are called ideal knots and ideal links respectively.

The ropelength problem is open: neither for knots nor for open knots in a long rope has an expression been found (in 2026) that describes the ropelength of tight, ideal knots. The problem is unsolved (in 2026) for every non-trivial knot.

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