Creating digits of pi

02212018, 11:01 AM
(This post was last modified: 02212018 04:39 PM by EdS2.)
Post: #61




RE: Creating digits of pi
(02172018 03:02 PM)Gerson W. Barbosa Wrote:(02172018 12:27 PM)EdS2 Wrote: I just came across this nice approximation, by Ramanujan (of course) Hmm, would a mathematical genius look at a decimal expansion? I would hope for some rather more sophisticated source of the insight  but do we know, or can we ever know, where this approximation came from? I can't resist sharing this other one from Ramanujan, which agrees to 18 digits apparently but with only 12 digits in the expression: \(\pi \approx \frac{12}{\sqrt{190}}\log\big((2\sqrt{2}+\sqrt{10})(3+\sqrt{10})\big)\) As continued fractions: 3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, ... vs 3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 1, 2, ... Edit: found this one in Ramanujan's papers  see TABLE II here. 

02232018, 01:34 PM
Post: #62




RE: Creating digits of pi
(02112018 12:12 AM)TASP Wrote: Yeah, not helpful at all, but for some random digit of Pi in base 2, just guess. For a single digit, yes. For multiple digits you need to be increasingly lucky. For 2 digits a guess may be correct 25% of the time. 3 digits, 12,5% of the time. 4 digits 6.25% etc... Wikis are great, Contribute :) 

02242018, 09:08 AM
Post: #63




RE: Creating digits of pi
(02212018 11:01 AM)EdS2 Wrote: I can't resist [...] If it is only about approximation the following is quite close: Code: /* This is Rexx */ In the result only every now and then a digit (4 altogether) differs from Pi. Ciao.....Mike 

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