4 ms·

No love for pi/4? It has (IMHO) the most beautiful infinite series: pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ...

• philthesong 13y ago
  Does pi/4 equal to tau/8?
  • jessriedel 13y ago
    Yes.
• gizmo686 13y ago
  If you re-arrange the terms, you can find that that series equals tau/4.
  • Retric 13y ago
    No, no you can't it's tau/8.
    • gizmo686 13y ago
      Its a conditionally convergent series; you can re-arrange the terms to add up to any real number you like (or diverge). [1]. [1]http://en.wikipedia.org/wiki/Conditional_convergence http://en.wikipedia.org/wiki/Conditional_convergence
      • Retric 13y ago
        You can construct a new series such that every term in the old one is there. However, if you try and rearrange the terms you end up with a backlog that coverages to the difference between the series. Which is why the actual series converges in the first place.