4 ms·

Pi is within 1% of 22/7. Edit: Another way of putting it, pi is not infinite. It's a number between 3.14 and 3.15.

• tgb 9y ago
  That's not entirely what they mean either, because then every irrational number is "close" to a rational (just take its decimal expansion out to 200 digits - that's rational and very close to the irrational number). You also have to consider the size of the denominator of the rational you are comparing to: i.e. you want to say that irrationals are close being ration if they're close to be a "nice" rational. Where 1/2 is clearly nicer than 22/7 which is clearly nicer than 257/139.
  • jfaucett 9y ago
    thank you! That makes sense.
  • asddkk 9y ago
    I think there's some information-theoretic ideas about compressibility or codelength that are relevant. The appeal, I think, is in being able to succinctly represent a random or irrational mathematical object with some other object that's not exactly the same, but is simpler to describe and equivalent to some high degree of similarity. Normally these ideas are applied to things that are thought of as random in a physically stochastic sense, but you could apply them to things that are random in an information-theoretic irrationality sense also. I'd say the polyhedra they discuss are kind of examples of this, maybe in reverse or something: they are simplified constructs that work as representations to some close extent. There's some interesting ties here to pseudorandom numbers, in that usually we think of them as approximating true randomness, even though they're entirely reproducible and predictable. This seems similar to me at some level.