(NOTE: It only does 18 iterations, as if you try to do any more, it raises an OverflowError, how lame.. -__-)
わーい, another π approximation method! (I do love these things. π is gorgeous, is it not?)
This is one of the fastest formulae for π out there, used to approximate out to 50 TRILLION DIGITS of π, in January of this year!
The notation for this in Σ is very long, so I have provided a screenshot of it, from its Wikipedia page:
Feedback is greatly appreciated, please enjoy!
If you are interested in learning more, this is the Wikipedia page:
(EDIT: Wow! I am glad this was a bit of a conversation starter for you all, thank you so much for all the upvotes!!)
(EDIT 2: I am still getting tons of traction on this, and am glad it is so interesting to all of you. Thank you so much!)