I'm taking an undergraduate level GR course, and from my text (Lambourne), the author describes a geodesic as a curve that "always goes in the same direction", and says that the tangent vector to the curve at some point u+du (where u is the parameter variable from which all the vector components of the space are defined) should be proportional to the parallel transported tangent vector on the same curve at the same point u+du. I'm trying to picture this connection on a great circle in spherical geometry, and I can't see the following: 1. How does the tangent vector always point in the same direction at all points on a great circle of a sphere? 2. How can the parallel transported vector point in the same direction as the tangent vector at all points on a great circle of a sphere? Could anyone show me with some sort of diagram? There is none in my text, and I'm really struggling with this. P.S. please forgive me if this is not the correct subforum for this type of post.