.... and proof of irrationality is not hard (Wikipedia has several), although certainly nontrivial. Proof that it's transcendental is, requiring e.g. abstract algebra (Lindemann-Weierstrass theorem).
Cheers, Bert On Tue, May 31, 2011 at 7:12 AM, Ravi Varadhan <rvarad...@jhmi.edu> wrote: > `pi' is more than irrational - it is transcendental, which mean it cannot be > the zero of a polynomial with integer coefficient. All transcendentals are > irrationals, but not vice-versa. > > I have also heard (courtesy: John Nash) that `pi' is the ratio of actual time > it takes to complete your thesis to the anticipated time. > > I have also heard that March 14 is the official `pi' day in the US (probably > not in Indiana!). > > Ravi. > > ------------------------------------------------------- > Ravi Varadhan, Ph.D. > Assistant Professor, > Division of Geriatric Medicine and Gerontology School of Medicine Johns > Hopkins University > > Ph. (410) 502-2619 > email: rvarad...@jhmi.edu > > > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On > Behalf Of Bentley Coffey > Sent: Monday, May 30, 2011 9:01 PM > To: Vincy Pyne > Cc: r-help@r-project.org > Subject: Re: [R] Value of 'pi' > > Pi is an irRATIOnal number, meaning that it is not equal to the ratio of any > integers ("whole numbers"). Hence, 22/7 is ONLY an approximation. The > built-in value for pi in R is also just an approximation (pi has no terminal > digit on the right of the decimal point so any finite number of digits will > just be an approximation). Yet, the built-in value for pi in R is a more > precise approximation, which is usually preferred... > On May 30, 2011 2:02 AM, "Vincy Pyne" <vincy_p...@yahoo.ca> wrote: >> Dear R helpers, >> >> I have one basic doubt about the value of pi. In school, we have learned > that >> >> pi = 22/7 (which is = 3.142857). However, if I type pi in R, I get pi = > 3.141593. So which value of pi should be considered? >> >> Regards >> >> Vincy >> >> >> >> >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > [[alternative HTML version deleted]] > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > -- "Men by nature long to get on to the ultimate truths, and will often be impatient with elementary studies or fight shy of them. If it were possible to reach the ultimate truths without the elementary studies usually prefixed to them, these would not be preparatory studies but superfluous diversions." -- Maimonides (1135-1204) Bert Gunter Genentech Nonclinical Biostatistics 467-7374 http://devo.gene.com/groups/devo/depts/ncb/home.shtml ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
