  Let Delta be a random spherical triangle (meaning that vertices are
independent and uniform on the unit sphere). A closed-form expression for the
area density of Delta has been known since 1867; a complicated integral
expression for the perimeter density was found in 1994. Does there exist a
closed-form expression for the latter? We attempt to answer this question from
several directions. An outcome of our work is the exact value of the perimeter
density at the point pi.
