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Thus if the spherical surface beings are living on a planet of

which the solar system occupies only a negligibly small part of

the spherical universe, they have no means of determining whether

they are living in a finite or in an infinite universe, because

the "piece of universe" to which they have access is in both

cases practically plane, or Euclidean. It follows directly from

this discussion, that for our sphere-beings the circumference of

a circle first increases with the radius until the "circumference

of the universe" is reached, and that it thenceforward gradually

decreases to zero for still further increasing values of the

radius. During this process the area of the circle continues to

increase more and more, until finally it becomes equal to the

total area of the whole "world-sphere."