  We compute Dirichlet eigenvalues and eigenfunctions explicitly for spherical
lunes and the spherical triangles which are half the lunes, and show that the
fundamental gap goes to infinity when the angle of the lune goes to zero. Then
we show the spherical equilateral triangle of diameter $\frac{\pi}{2}$ is a
strict local minimizer of the fundamental gap on the space of the spherical
triangles with diameter $\frac{\pi}{2}$, which partially extends Lu-Rowlett's
result from the plane to the sphere.
