"Euclid assumes that parallel lines never meet, which they cannot
do of course if they be defined as equidistant. But are there such
lines? And if not, why not assume that all lines drawn through a
point outside a given line will eventually intersect it? Such an
assumption leads to a geometry in which all lines are conceived as
being drawn on the surface of a sphere or an ellipse, and in it the
three angles of a triangle are never quite equal to two right angles,
nor the circumference of a circle quite [pi] times its diameter. But
that is precisely what the contraction effect due to motion requires."
(Dr. Walker)