Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Position of the centroid of a planar convex body and the centroid
  Banach-Mazur distance   It is well known that any planar convex body $A$ permits to inscribe an
affine-regular hexagon $H_A$. We prove that the centroid of $A$ belongs to the
homothetic image of $H_A$ with ratio $\frac{4}{21}$ and the center in the
center of $H_A$.This ratio cannot be enlarged. Moreover, we consider the
variant of the Banach-Mazur distance $\delta_{BM}^{\rm cen} (C, D)$ of two
convex bodies $C, D$ of $E^d$ with the additional requirement that the
centroids of them coincide. We prove that $\delta_{BM}^{\rm cen} (C, D) \leq
\frac{33}{8}$ for every $C, D$ of $E^2$.

28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int