Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An estimation of the Moon radius by counting craters: a generalization
  of Monte-Carlo calculation of $\pi $ to spherical geometry   By applying Monte-Carlo method, the Moon radius is obtained by counting
craters in a spherical square over the surface of it. As it is well known,
approximate values for $\pi $ can be obtained by counting random numbers in a
square and in a quarter of circle inscribed in it in Euclidean geometry. This
procedure can be extend it to spherical geometry, where new relations between
the areas of a spherical square and the quarter of circle inscribed in it are
obtained. When the radius of the sphere is larger than the radius of the
quarter of circle, Euclidean geometry is recovered and the ratio of the areas
tends to $\pi $. Using these results, theoretical deviations of $\pi $ due to
the Moon radius $R$ are computed. In order to obtain this deviation, a
spherical square is selected located in a great circle of the Moon. The random
points over the spherical square are given by a specific zone of the Moon where
craters are distributed almost randomly. Computing the ratio of the areas, the
deviation of $\pi $ allows us to obtain the Moon radius with an intrinsic error
given by the finite number of random craters.

28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin