I briefly looked into the section on general relativity and did not find the explanation particularly enlightening. A proper entirely geometrical description of

I briefly looked into the section on general relativity and did not find the explanation particularly enlightening. A proper entirely geometrical description of curvature can be found in Mathematical Methods of Classical Mechanics (p. 301 ff.) by Arnold, although it is probably not accessible to a lay person. Penrose's "The Road to Reality" should be more accessible and seems to be of higher quality than the web site linked.