# Tagged Questions

**1**

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**1**answer

106 views

### Bitangent locus of torus knots

Anyone know how to compute the bitangent locus of a space curve, e.g. a torus knot (pick whatever parametrization you like)? Specifically, what is the set of normal vectors (in the two-sphere) of ...

**3**

votes

**1**answer

117 views

### Some questions about ideal knots

The ropelength of a knot curve $C$ is defined as the ratio $L(C) = \lambda(C)/ \tau(C)$, where $\lambda(C)$ is the length of $C$ and $\tau(C)$ is the thickness of the knot defined by $C$ [from ...

**5**

votes

**1**answer

315 views

### Euclidean symmetries of torus links in R^3

I have a question about whether Ryan Budney's question:
Torus knots in Euclidean space -- a symmetry argument
can be extended to links. He asks:
Suppose you have a $(p,q)$ torus knot $K$ in ...

**1**

vote

**1**answer

384 views

### What is the shape of a tight open trefoil?

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 ...

**8**

votes

**2**answers

1k views

### Slice knots and exotic $\mathbb R^4$

In the http://arxiv.org/abs/math/0606464v1 I read
"If you want to prove existence of exotic smooth structure on $\mathbb R^4$ you can do this if you are in
possession of a knot which is ...

**8**

votes

**1**answer

728 views

### The total curvature of very knotty knots

One of my favorite theorems is that of Fáry-Milnor, stating that the total curvature of a knot in $\mathbb R^3$ which is not an unknot (an ununknot) is at least $4\pi$.
Can one quantify the way in ...