4 ms·

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 to

by mb7733 6y ago

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.

amelius 6y ago
But the title says "... and its Applications". Is tying actual knots not an application of knot theory?
- gjm11 6y ago
  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.)
- mb7733 6y ago
  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.
  - kortex 6y ago
    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://en.m.wikipedia.org/wiki/Link_(knot_theory) https://math.stackexchange.com/questions/217670/is-there-a-mathematical-theory-of-physical-knots https://math.stackexchange.com/questions/217670/is-there-a-m... https://en.m.wikipedia.org/wiki/Physical_knot_theory https://en.m.wikipedia.org/wiki/Physical_knot_theory
mathgenius 6y ago
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 https://en.wikipedia.org/wiki/Perko_pair
- deleted 6y ago
  [deleted]
jpcooper 6y ago
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.

by mb7733 6y ago

amelius 6y ago

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

gjm11 6y ago
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.)
mb7733 6y ago
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.
- kortex 6y ago
  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://en.m.wikipedia.org/wiki/Link_(knot_theory) https://math.stackexchange.com/questions/217670/is-there-a-mathematical-theory-of-physical-knots https://math.stackexchange.com/questions/217670/is-there-a-m... https://en.m.wikipedia.org/wiki/Physical_knot_theory https://en.m.wikipedia.org/wiki/Physical_knot_theory

mathgenius 6y ago

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 https://en.wikipedia.org/wiki/Perko_pair

deleted 6y ago
[deleted]

jpcooper 6y ago

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.