  The inner product provides a conceptually and algorithmically simple method
for calculating the comoving distance between two cosmological objects given
their redshifts, right ascension and declination, and arbitrary constant
curvature. The key to this is that just as a distance between two points `on'
the surface of the ordinary 2-sphere ${\cal S}^2$ is simply an arc-length
(angle multiplied by radius) in ordinary Euclidean 3-space ${\cal E}^3$, the
distance between two points `on' a 3-sphere ${\cal S}^3$ (a 3-hyperboloid
${\cal H}^3$) is simply an `arc-length' in Euclidean 4-space ${\cal E}^4$
(Minkowski 4-space ${\cal M}^4$), i.e. an `hyper-angle' multiplied by the
curvature radius of the 3-sphere (3-hyperboloid).
