Talk:Mathematical constants by continued fraction representation
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editHi
Is it possible to get a square root of 3 function to insert in the list?
Regards
adamlewis1960@yahoo.com.au
- As a first step, one could simply evaluate sqrt(3) on any calculator to give approx. 1.732050808... Then go to an online tool such as this Online Solver for Continued Fractions and enter the approx. decimal value. For the given accuracy, you would obtain [1; 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 8, 1, ...]. However, the final few entries are due to the fact, that the decimal value is approx and not exact. For sqrt(3), the apparent pattern strongly suggests, that the sequence [1, 2] is repeated infinitely. Gulliveig (talk) 06:00, 21 June 2008 (UTC)
Continued Fraction Representation
editWhy is there an entry [0;1,1] for the number 1/2? [0;1,1] = 0+1/(1+1/1), but it is clear that this resolves to [0;2] = 0+1/2, which has an entry as well. The final 1/1 introduces an absolutely unneeded fraction, which makes the whole entry unneeded. However, if there is a reason which escapes me so far, please enlighten me. Gulliveig (talk) 05:38, 21 June 2008 (UTC)
- Any finite continued fraction ending in a 1: is equivalent to a continued fraction one element shorter: . In particular, [0;1,1] = [0;2], as you say. -68.191.214.241 (talk) 21:18, 13 December 2008 (UTC)
![{\displaystyle \left[a_{0};a_{1},\ldots ,a_{n-1},1\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6886bbfc6462566db5395320d77ec5dd2cb7d93b)
![{\displaystyle \left[a_{0};a_{1},\ldots ,a_{n-1}+1\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/013f726e722a66c7b9fdd3d3551f8d1c484e0f11)
Table of continued fractions
editTo de-clutter list of mathematical constants, I removed columns containing continued fraction representations. Hence the continued fractions can be easily copied over from here: https://en.wikipedia.org/w/index.php?title=List_of_mathematical_constants&diff=898237523&oldid=897226620
If anyone would like to expand Mathematical constants by continued fraction representation, they should do so by copying over the aforementioned continued fractions. Jamgoodman (talk) 16:26, 29 May 2019 (UTC)