a.) On a hyperbolic plane, consider the curves that run radially across each annular strip. Argue that these curves are intrinsically straight. Also, show that any two of them are asymptotic, in the sense that they converge towards each other but do not intersect.
b.) Find other geodesics on your physical hyperbolic surface. Use the properties of straightness (such as symmetries).
c.) What properties do you notice for geodesics on a hyperbolic plane? How are they the same as geodesics on the plane or spheres, and how are they different from geodesics on the plane and spheres?