  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.
