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Comment by mb7733 | Hacker News Reader

I think learning and tying knots is cool too, but just a heads up, the mathematical knot theory discussed in the OP is not related to that. It's a branch of topology that studies the possible shapes and transformations of closed curves in 3-space (without self intersection).

It's not concerned with practical properties of knots tied with rope, like strength, stability, ease of use, etc.

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Of course they are related! A knot is a knot. It's just that mathematicians are obsessed with proving things rigorously [1], whereas the sailor just wants his sails to hang right.

[1] https://en.wikipedia.org/wiki/Perko_pair

But the title says "... and its Applications". Is tying actual knots not an application of knot theory?

The applications mentioned in the book are to chemistry and to molecular biology. (As well as another, mentioned only fairly briefly, elsewhere in pure mathematics, to what's called the classification of 3-manifolds.)

No, tying knots isn't an application of knot theory. To learn about some applications of knot theory, you could read the textbook in the OP.

It is absolutely related, though most real world things we call knots are usually in fact closer to tangles or links with the ends of the rope looping back to the other end virtually.

Neck ties are a mathematical knot if you again assume the two ends are connected. See other comment in this thread.

Knot theory here only determines the "shapes" of the knots and which are "allowed", there is no friction, width, etc.

https://en.m.wikipedia.org/wiki/Link_(knot_theory)

https://math.stackexchange.com/questions/217670/is-there-a-m...

https://en.m.wikipedia.org/wiki/Physical_knot_theory

Not only 3-space. An example of a slice knot would be a normal 1-dimensional knot suspended in 3-space which turns out to be the 3-dimensional slice/cross-section of a 2-dimensional sphere suspended and knotted in 4-space.

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