The conclusion is that they are useless, but this is predicated on a notion that there is some use to which they can be put. The "trend" therefore is not what matters - who cares if I can't find a hugely accurate rational form past what I couldn't remember anyway? What matters is those few near the start. He dismisses 22/7 as being no better than 3.14 because it only agrees in the same number of digits; it is in fact more accurate, and easier to use for some operations. 355/113 is not only easier to remember but also substantially more accurate than the decimal approximation with the same number of digits. Rarely will you need more accuracy than that in your head (or on your napkin). If you need more in your program, M_PI is also 4 characters...
