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Take an infinitely long rope of diameter 1, ideally flexible and ideally slippery. Tie a trefoil knot into it and pull it tight. Describe the resulting rope shape analytically.

The problem is unsolved for every non-trivial open knot. (And also for every closed non-trivial knot.) Solving it seems extremely hard.

The above question was closed; this is an attempt to change this:

Is there at least a practical analytical approximation for the shape of the tight open trefoil? Maybe one whose shape is known to be at most within a certain suitably defined distance from the exact solution?

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And... ? –  Qfwfq May 3 '11 at 12:12
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MathOverflow is "for questions that have answers". In the body of your question, you make the claim that this problem has no (known) answer. If that's indeed the case, then this is no an appropriate MathOverflow question. If you want to know whether the answer is known and, if yes, what the answer is, then I suggest that you rephrase your question differently. –  André Henriques May 3 '11 at 13:42
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MathOverflow is not a place for collecting and sharing well-known open problems. Please see the FAQ. –  S. Carnahan May 3 '11 at 14:04
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I voted to reopen this. As far as I can tell, Nemo is not sharing an open question -- he is observing that the determination of the optimal solution is an open question, and asking whether any solution is known that is provably within epsilon of optimal. That's a real question, as far as I can see. –  JSE May 3 '11 at 20:41
    
There is an optimal configuration for every knot, popularized by Michael Freedman, see $$ $$ mathoverflow.net/questions/32245/… –  Will Jagy May 4 '11 at 1:32
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1 Answer

As far as I know people don't have an answer to your question. The people that perhaps have the best sense for the answer to your question would be Canterella, Kusner and Sullivan. Relevant reference:

http://front.math.ucdavis.edu/1102.3234

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