I am guessing that an algorithm to extract the nth term for the continued fraction of pi is *harder* than an algorithm to extract the nth digit. Consider: The first term of the continued fraction of x is floor(x). The second term is floor(1/(x-floor(x))). Can one calculate that directly, without calculating floor(x) first? It doesn't seem likely. On Fri, Mar 15, 2019 at 3:25 PM Dan Asimov <dasimov@earthlink.net> wrote:
What might be interesting would be to see kajillions of "digits" of the continued fraction expansion (CFE) of π. At least, that's independent of how many fingers we have.
Are there good algorithms for calculating a high "digit" of the CFE of π without knowing the previous ones?
—Dan
Simon Plouffe schrieb: ----- Pi has been calculated to 31.4 trillion digits : http://www.numberworld.org/blogs/2019_3_14_pi_record/
they used the Chudnovsky formula, the Bellard formula and mine just to be certain. -----
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