Seite 171 von 212

i.e. a smaller value than π, the difference being the more

considerable, the greater is the radius of the circle in

comparison with the radius R of the "world-sphere." By means of

this relation the spherical beings can determine the radius of

their universe ("world"), even when only a relatively small part

of their worldsphere is available for their measurements. But if

this part is very small indeed, they will no longer be able to

demonstrate that they are on a spherical "world" and not on a

Euclidean plane, for a small part of a spherical surface differs

only slightly from a piece of a plane of the same size.