Lune (Surface)

$\begin{figure}\begin{center}\BoxedEPSF{LuneSurface.epsf}\end{center}\end{figure}$

A sliver of the surface of a Sphere of Radius cut out by two planes through the azimuthal axis with Dihedral Angle $\theta$ . The Surface Area of the lune is

$\begin{displaymath} S=2r^2\theta, \end{displaymath}$

which is just the area of the Sphere times $\theta/(2\pi)$ .

See also Lune (Plane), Sphere

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 130, 1987.