The Manga Guide to the Universe

232 Chapter 5 Our Ever-Expanding Universe

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 ...