# Tagged Questions

**14**

votes

**2**answers

244 views

### Random rings linked into one component?

Let $S$ be a sphere of unit radius.
Let $C_n$ be a collection of unit-radius circles/rings whose centers
are (uniformly distributed)
random points in $S$, and which are oriented (tilted) randomly ...

**2**

votes

**2**answers

331 views

### Infinite knot composed of parallel helices

I am wondering if there is a developed theory of "infinite knots" that could capture
this object, and tell me something of its knot properties.
Imagine vertical helices in $\mathbb{R}^3$, each ...

**9**

votes

**3**answers

448 views

### Circle-arc number of a knot

I would like to build knots in $\mathbb{R}^3$ from arcs
of unit-radius (planar) circles, joined together at points where
the tangents match. Thus the knot will have
curvature $1$ at all but the ...

**5**

votes

**2**answers

359 views

### Tangled Knot Function

I am seeking a function $f: \mathbb{R}^3 \to \mathbb{R}^3$
that has these properties:
(1) When iterated $n$ times starting from some $p$,
connecting the points in order
with segments and closing ...

**2**

votes

**2**answers

381 views

### Is it possible to reliably generate a particular approximation of an ideal knot via a simulated annealing approach?

Say I take a cord, tie a loose knot in three-dimensional space, and pull tightly on the ends to generate an approximation of an ideal knot. If the cord has a fixed knot topology and a random initial ...

**46**

votes

**4**answers

3k views

### Tying knots with reflecting lightrays

Let a lightray bounce around inside a cube whose faces
are (internal) mirrors.
If its slopes are rational, it will eventually form a cycle.
For example, starting with a point $p_0$ in the interior
of ...

**6**

votes

**2**answers

572 views

### Lattice Stick Number vs. Stick Number of Knot

Can the lattice stick number of a knot be bounded
by the stick number of the knot?
The stick number
$S(K)$ of a knot $K$ is the fewest number of segments
needed to realize it by a simple 3D ...