Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inscribed rectangles in a smooth Jordan curve attain at least one third
  of all aspect ratios   We prove that for every smooth Jordan curve $\gamma$, if $X$ is the set of
all $r \in [0,1]$ so that there is an inscribed rectangle in $\gamma$ of aspect
ratio $\tan(r\cdot \pi/4)$, then the Lebesgue measure of $X$ is at least $1/3$.
To do this, we study disjoint M\"obius strips bounding a $(2n,n)$-torus link in
the solid torus times an interval. We prove that any such set of M\"obius
strips can be equipped with a natural total ordering. We then combine this
total ordering with some additive combinatorics to prove that $1/3$ is a sharp
lower bound on the probability that a M\"obius strip bounding the $(2,1)$-torus
knot in the solid torus times an interval will intersect its rotation by a
uniformly random angle.

22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci