Assuming that we construct a link/chain using a collection of knots.
Is there a way to measure the physical strength of this chain?
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2$\begingroup$ What sort of underlying physical assumptions are you making here? $\endgroup$– David Roberts ♦Commented Sep 3, 2015 at 7:32
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$\begingroup$ For example, let us assume that two chains are made of the same material but have different knotting topologies. I would like to evaluate their resistance to deformation/breaking based on the knottings. $\endgroup$– RaskolCommented Sep 3, 2015 at 7:52
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3$\begingroup$ This requires a lot more assumptions to make sense... $\endgroup$– Igor RivinCommented Sep 3, 2015 at 8:55
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1$\begingroup$ @Raskol what about elasticity? Flexibility? Compressibility? Friction? Mass? Radius? The study of physical knots (i.e. embeddings of knotted solid tori) is actually quite complicated without making it an engineering problem, too. $\endgroup$– David Roberts ♦Commented Sep 3, 2015 at 10:32
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There is one problem along these lines that allows for some rather precise mathematical statements: What is the condition for a hitch to hold? A hitch is a knot around a rigid object (a pole). Because the pole is not compressible, and assumed to be much thicker than the rope, the problem whether or not the knot holds (meaning, friction wins no matter how hard you pull on the rope) can be formulated and solved as a problem in linear algebra:
answered Sep 3, 2015 at 10:43
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5$\begingroup$ The answer is better than the question :) $\endgroup$ Commented Sep 3, 2015 at 10:51