Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivative relationships between volume and surface area of compact
  regions in R^d   We explore the idea that the derivative of the volume, V, of a region in R^d
with respect to r equals its surface area, A, where r = d V/A. We show that the
families of regions for which this formula for r is valid, which we call
homogeneous families, include all the families of similar regions. We determine
equivalent conditions for a family to be homogeneous, provide examples of
homogeneous families made up of non-similar regions, and offer a geometric
interpretation of r in a few cases.

17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas