ABSTRACT
This chapter discusses the appear unpleasantly technical to the reader and certainly in contrast to the tone of most of the text so far. However, in this specific instance, this is the case, at least primarily, for the motivation behind the whole technical arsenal is one stemming from Physics, more specifically from General Relativity. A different, quite natural, approach to the estimation of curvatures of smooth manifolds by the discrete curvature of piecewise flat approximations stems from Definition 2.2.12. Besides the rather technical approaches we detailed above, and which are of great importance primarily on the theoretical side, there exist a number of other approaches, perfect easier to implement in applications and some which were devised precisely toward such ends.
