Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Distances Associated With Equilateral Triangles   In this report, the explicit probability density functions of the random
Euclidean distances associated with equilateral triangles are given, when the
two endpoints of a link are randomly distributed in 1) the same triangle, 2)
two adjacent triangles sharing a side, 3) two parallel triangles sharing a
vertex, and 4) two diagonal triangles sharing a vertex, respectively. The
density function for 1) is based on the most recent work by Basel [1]. 2)-4)
are based on 1) and our previous work in [2], [3]. Simulation results show the
accuracy of the obtained closed-form distance distribution functions, which are
important in the theory of geometrical probability. The first two statistical
moments of the random distances and the polynomial fits of the density
functions are also given in this report for practical uses.

17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat