SIDELIGHTS ON RELATIVITY

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From the latest results of the theory of relativity it is probable
that our three-dimensional space is also approximately spherical,
that is, that the laws of disposition of rigid bodies in it are
not given by Euclidean geometry, but approximately by spherical
geometry, if only we consider parts of space which are sufficiently
great. Now this is the place where the reader's imagination boggles.
"Nobody can imagine this thing," he cries indignantly. "It can be
said, but cannot be thought. I can represent to myself a spherical
surface well enough, but nothing analogous to it in three dimensions."

[Figure 2: A circle projected from a sphere onto a plane]

We must try to surmount this barrier in the mind, and the patient
reader will see that it is by no means a particularly difficult
task. For this purpose we will first give our attention once more to
the geometry of two-dimensional spherical surfaces. In the adjoining
figure let _K_ be the spherical surface, touched at _S_ by a plane,