We have already seen that different curvatures of space cause the geometry of a trian-
gle to change (see Figure 5-5). On a flat surface, parallel lines remain parallel, meaning that
the edges of a triangle are straight and the angles of the triangle add up to 180 degrees. On
a closed (spherical) surface, parallel lines converge so that a triangle’s lines bend outward
and the angles of the triangle add up to something greater than 180 degrees. On an open
(saddle-shaped) surface, parallel lines bend apart so that a triangle’s lines bend inward and
the angles of the triangle add up to less than 180 degr ...
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