There are surfaces in which geodesics coincide with the usual euclidean concept of straight line. One of these is the one sheet hyperboloid. This surface can be obtained by revolution of a traditional hyperbola. The important fact here is that it contains an infinity amount of lines. However, the one sheet hyperboloid is not a flat surface. So, in order to study flatness of universe, searching for euclidean lines as geodedics may be not enough. As you might know from the last post (level 6) you have to find geodesic triangles a measure its angles.