Creating digits of pi
|
02-21-2018, 11:01 AM
(This post was last modified: 02-21-2018 04:39 PM by EdS2.)
Post: #43
|
|||
|
|||
RE: Creating digits of pi
(02-17-2018 03:02 PM)Gerson W. Barbosa Wrote:(02-17-2018 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. |
|||
« Next Oldest | Next Newest »
|
User(s) browsing this thread: 1 Guest(s)