This paper discusses the distribution of the non-trivial zeros of the Riemann zeta function ζ. It looks into the question of whether any non-trivial zeros would ever possibly be found off the critical line Re(s) = 1/2 on the critical strip between Re(s) = 0 and Re(s) = 1, e.g., at Re(s) = 1/4, 1/3, 3/4, 4/5, etc., and why all the non-trivial zeros are always found at the critical line Re(s) = 1/2 on the critical strip between Re(s) = 0 and Re(s) = 1 and not anywhere else on this critical strip, with the first 1013 non-trivial zeros having been found only at the critical line Re(s) = 1/2. It should be noted that a conjecture, or, hypothesis could possibly be proved by comparing it with a theorem that has been proven, which is one of the several deductions utilized in this paper. Through these several deductions presented, the paper shows how the Riemann hypothesis may be approached to arrive at a solution. In the paper, instead of merely using estimates of integrals and sums (which are imprecise and may therefore be of little or no reliability) in the support of arguments, where feasible actual computations and precise numerical facts are used to support arguments, for precision, for more sharpness in the arguments, and for "checkability" or ascertaining of the conclusions. [Published in international mathematics journal.]