SIDELIGHTS ON RELATIVITY

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surface, we have an uninterrupted disposition in which there are
six discs touching every disc except those which lie on the outside.

[Figure 1: Discs maximally packed on a plane]

On the spherical surface the construction also seems to promise
success at the outset, and the smaller the radius of the disc
in proportion to that of the sphere, the more promising it seems.
But as the construction progresses it becomes more and more patent
that the disposition of the discs in the manner indicated, without
interruption, is not possible, as it should be possible by Euclidean
geometry of the the plane surface. In this way creatures which
cannot leave the spherical surface, and cannot even peep out from
the spherical surface into three-dimensional space, might discover,
merely by experimenting with discs, that their two-dimensional
"space" is not Euclidean, but spherical space.