Observational Cosmology - Unit 2 Solutions

4. Sketches will help a lot here:
(a) The angles of a triangle sum to >180o in the case of a sphere (+ve curvature) and <180o for a saddle (-ve curvature). See RR Fig.4.6  or Liddle Fig 5.1
(b) Parallel lines converge and cross on a sphere, and diverge on a saddle.
(c) The circumference of a circle is <2.pi.r on a sphere, and >2.pi.r on a saddle (consider trying to flatten the circle onto a flat surface).