SIDELIGHTS ON RELATIVITY

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a quantity of small paper discs, all of the same size. We place
one of the discs anywhere on the surface of the globe. If we move
the disc about, anywhere we like, on the surface of the globe,
we do not come upon a limit or boundary anywhere on the journey.
Therefore we say that the spherical surface of the globe is an
unbounded continuum. Moreover, the spherical surface is a finite
continuum. For if we stick the paper discs on the globe, so that
no disc overlaps another, the surface of the globe will finally
become so full that there is no room for another disc. This simply
means that the spherical surface of the globe is finite in relation
to the paper discs. Further, the spherical surface is a non-Euclidean
continuum of two dimensions, that is to say, the laws of disposition
for the rigid figures lying in it do not agree with those of the
Euclidean plane. This can be shown in the following way. Place
a paper disc on the spherical surface, and around it in a circle
place six more discs, each of which is to be surrounded in turn
by six discs, and so on. If this construction is made on a plane