From Newsgroup: comp.misc
yeti <
yeti@tilde.institute> wrote or quoted:
I haven't seen this update yet. So far I only bookmarked it in my RSS
feeds for somewhen later.
There was a time when mathematicians believed it was impossible
to calculate a specific digit of pi without computing all
preceding digits. This belief persisted until the discovery of
the Bailey–Borwein–Plouffe (BBP) formula in 1995. The BBP formula
allows for the extraction of any arbitrary digit of pi in its
binary expansion (base 2) without calculating prior digits.
This was groundbreaking and contrary to earlier assumptions.
In 1996, Simon Plouffe extended this concept to base 10, enabling
the calculation of specific decimal digits of pi without computing
all preceding digits, though at a computational cost of O(n^3 (log
n)^3), later improved to O(n^2) by Fabrice Bellard. Before these
developments, no such efficient "digit extraction" algorithms were
known, and it was widely assumed that such methods were not possible.
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