Can knots be described mathematically?

[Rum]

A bow for example, it occurred to me as I took my walking boots off, is a thing of symmetry and with rules. So I wondered it it, and other knots can be described with maths.

[Clinton Huxley]

Yes, yes they can.

[normal]

Knot on my watch!

[Clinton Huxley]

It's a knotty problem and I believe some of the loose ends are still to be tied up.

[klr]

I suspect the answer is probably "yes", but that's just an intuitive guess. Like many people, I don't even have to consciously think when tying my shoelaces, so it's not something I've ever pondered deeply about.

[Clinton Huxley]

I believe that Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces, but I'm no expert.

[Atheist-Lite]

Knots, braids, bends, links, hitches, weaves etc. are described by d-dimensional space-curves. Their projections can be shown as 2D shadows, 2.5D knot diagrams, and 3D tubes using piece-wise cubic interpolation. Mathematical knots and links are closed 3D lines that cannot be untangled without passing lines through lines. Braids provide compact knot descriptors; bends join two ropes; hitches and binding knots are tied round posts etc.
-Roger Bereford, mathematics geek.

http://mathworld.wolfram.com/KnotTheory.html

Knot Theory

The mathematical study of knots. Knot theory considers questions such as the following:

1. Given a tangled loop of string, is it really knotted or can it, with enough ingenuity and/or luck, be untangled without having to cut it?

2. More generally, given two tangled loops of string, when are they deformable into each other?

3. Is there an effective algorithm (or any algorithm to speak of) to make these determinations?

Although there has been almost explosive growth in the number of important results proved since the discovery of the Jones polynomial, there are still many "knotty" problems and conjectures whose answers remain unknown.

etc, etc, follow links. All about topology. Why is the obvious so hard?

[Bella Fortuna]

Not the Mathematician (He's a Very Knotty Boy)

[Clinton Huxley]

There are knot the answers Rum was hoping for

[Bella Fortuna]

There are knot the answers Rum was hoping for

A-Gordian to you he should be getting something different?

[Clinton Huxley]

There are knot the answers Rum was hoping for

A-Gordian to you he should be getting something different?

A cutting remark.

[Bella Fortuna]

There are knot the answers Rum was hoping for

A-Gordian to you he should be getting something different?

A cutting remark.

I can't beweave you would say such a thing.

[Gawdzilla Sama]

I believe that Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed canonically into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces, but I'm no expert.

Spoiler that shit!

[Clinton Huxley]

There are knot the answers Rum was hoping for

A-Gordian to you he should be getting something different?

A cutting remark.

I can't beweave you would say such a thing.

Don't get your knickers in a twist

[Gawdzilla Sama]

Knot another pun-fest.