4 ms·
I don’t think anyone is impressed by how easy it is to store the symbolic representation of the fraction versus the symbolic representation of the first n digit
by tshaddox 4y ago
I don’t think anyone is impressed by how easy it is to store the symbolic representation of the fraction versus the symbolic representation of the first n digits of pi, or suggesting that it’s a useful way for humans to memorize or calculate pi. What’s notable is simply how close the fraction approximates the irrational number pi given how low the fraction’s denominator is.
- Nomentatus 4y agoBut he just gave you another example of just that. So that feature simply isn't unique.
- tshaddox 4y agoWhat other example has a similarly low denominator but gives as good or better accuracy than 355/133? I’m under the impression that there aren’t any such examples.
- Nomentatus 4y agoHe gave "355/113-1/3748629 has you memorize 17 digits to get pi to 16 digits." This is a compression problem, a little more breakage here or there is to be expected. If e and every other irrational number showed similar breakage, then I might get interested.
- alanbernstein 4y ago22/7 and 355/113 are both special in that the approximation error, relative to the denominator side, is unusually low. Pi is special in that it has even one such small-denominator approximation.