Re: [math-fun] cos(x) = x question
Simon Plouffe wrote:
Hello,
Yes, this is the argument, the length of the proposed approximation is about the length in number of digits of precision.
Indeed, the Elias (or Levenshtein) codes for 160 and 13 by themselves almost cover the 21 bits of precision, no code space is left for pi or the operations.
Just a coincidence, and there are others, very few can be explained fully.
here are a few of them : http://mathworld.wolfram.com/AlmostInteger.html
It used to be there; now it is mentioned here: http://mathworld.wolfram.com/DottieNumber.html
http://fr.wikipedia.org/wiki/Nombre_presque_entier (in french),
Thank you, Leo
If you haven't seen this it's worth reading: strange series and high precision fraud by the borweins http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P56.pdf Victor
On Aug 25, 2014, at 16:45, Leo Broukhis <leob@mailcom.com> wrote:
Simon Plouffe wrote:
Hello,
Yes, this is the argument, the length of the proposed approximation is about the length in number of digits of precision.
Indeed, the Elias (or Levenshtein) codes for 160 and 13 by themselves almost cover the 21 bits of precision, no code space is left for pi or the operations.
Just a coincidence, and there are others, very few can be explained fully.
here are a few of them : http://mathworld.wolfram.com/AlmostInteger.html
It used to be there; now it is mentioned here: http://mathworld.wolfram.com/DottieNumber.html
http://fr.wikipedia.org/wiki/Nombre_presque_entier (in french),
Thank you, Leo _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I also love this example in another similar paper: < http://en.wikipedia.org/wiki/Borwein_integral >. --Dan On Aug 25, 2014, at 1:50 PM, Victor S. Miller <victorsmiller@gmail.com> wrote:
If you haven't seen this it's worth reading: strange series and high precision fraud by the borweins http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P56.pdf
Yes, these examples are easy to make, like this one : infinity ----- \ / 1304 \ ) |-------------------| / | 2 | ----- \4 n - 4 n + 106277/ n = 1 is equal to Pi at 443 digits, if you see the pattern then you can push the approximation to billions of digits. Best regards, Simon Plouffe
participants (4)
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Dan Asimov -
Leo Broukhis -
Simon Plouffe -
Victor S. Miller