DISCOVERING APPROXIMANTS

Eddington ratio mathematical approximants were discovered by dividing the actual number of the given Eddington ratio by a known mathematical value that is special like e or pi or phi. What is left over, in division, was another such number like e or pi or phi or a surd like square roots of 2 or 3 etc. Once I figured out one of these this way, the other 4 were thus easy to figure out. The only way to do such calculations is (a) with a slide rule or (b) with a scientific calculator. I used a slide rule in high school but I do not know how to use one now...and so I bought a scientific calculator and used it carefully.