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 $1$ …

Let $C_N$ denote the labelled configuration of $N^{th}$ roots of unity with $p_J = e^{\frac{2\pi iJ}{N}}$ for $J = 1\ldots N$. As a corollary of something else I was playing aroun …

Does every polyhedron in $\mathbb{R}^3$ with $n$ triangular facets have a topological triangulation with complexity $O(n)$? Suppose $P$ is a non-convex polyhedron in $\mathbb{R}^3 …

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 segm …

I am seeking literature on 3D orthogonal drawings of knots, especially minimum bend drawings. An orthogonal drawing employs segments parallel to the axes of a Cartesian coordinate …

Suppose one has a knot $K$ embedded in $\mathbb{R}^3$; but view $\mathbb{R}^3$ as a 3-flat in $\mathbb{R}^4$. Of course $K$ is not a knot in $\mathbb{R}^4$. I am wondering if there …

Connect $n$ random points on a sphere in a cycle of segments between succesive points:       I would like to know the growth rate, with respect to $n$, o …

This question on physics stackexchange http://physics.stackexchange.com/questions/12973/the-entropic-cost-of-tying-knots-in-polymers has a formulation which is perhaps more appropr …

Looking at a table of minimum stick numbers for knots (table here), it seems the known upper bound of $2 c(K)$ in terms of the knot crossing number $c(K)$ is realized by the trefo …

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 stick knot is a just a piecewise linear knot. We could define "stick isotopy" as isotopy that preserves the length of each linear piece. Are there stick knots which are topologi …