, but for a given value of
it is the same for all points of the "world-sphere"; in other words, the "world-sphere" is a "surface of constant curvature."
To this two-dimensional sphere-universe there is a three-dimensional analogy, namely, the three-dimensional spherical space which was discovered by Riemann. Its points are likewise all equivalent. It possesses a finite volume, which is determined by its "radius" (
). Is it possible to imagine a spherical space? To imagine a space means nothing else than that we imagine an epitome of our "space" experience, i.e. of experience that we can have in the movement of "rigid" bodies. In this sense we can imagine a spherical space.
Suppose we draw lines or stretch strings in all directions from a point, and mark off from each of these the distance
with a measuring-rod. All the free end-points of these lengths lie on a spherical surface. We can specially measure up the area (