4 ms·
What's a nice infinite series summing to tau that isn't merely 2S(n) where S(n) sums to pi?
by thanatropism 10y ago
What's a nice infinite series summing to tau that isn't merely 2S(n) where S(n) sums to pi?
- thanatropism 10y agoHa. I've said a lot of continental-philosophy stuff that gets downvoted by the techie culture, but this is amazing.
- Bromskloss 10y agoJust checking: Do you mean that your comment amounts to continental philosophy?
- thanatropism 10y agoI'm saying this comment should be far less contentious than my comments that somehow cite Heidegger or Deleuze.
- andrewla 10y agoThe simplest formula that I can think of is pi/4 = tau/8 = atan(1) = 1 - 1/3 + 1/5 - 1/7 + ... 4 vs 8 doesn't seem like a change in the arbitrariness of the constant. The other major simple ones are: pi^2 / 6 = tau^2 / 24 = 1 + 1/(2^2) + 1/(3^2) + 1/(4^2) + ... pi^2 / 12 = tau^2 / 48 = 1 - 1(/2^2) + 1/(3^2) - 1/(4^2) + ... Once again, 6 vs 24 (and 12 vs 48) is an arbitrary difference in arbitrariness. I'm not really aware of any commonly used series expansions that don't involve a constant multiply just to get to pi. On the other hand, I'm not aware of anything super-elegant that yield tau here either, so I think it's a tie at best.