Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perimeter approximation of convex discs in the hyperbolic plane and on
  the sphere   Eggleston (1957) proved that in the Euclidean plane the best approximating
convex $n$-gon to a convex disc $K$ is always inscribed in $K$ if we measure
the distance by perimeter deviation. We prove that the analogue of Eggleston's
statement holds in the hyperbolic plane, and we give an example showing that it
fails on the sphere.

4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn