[R] Value of 'pi'

[Bert Gunter]

....
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 <rvaradhan at 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: rvaradhan at jhmi.edu
>
>
> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Bentley Coffey
> Sent: Monday, May 30, 2011 9:01 PM
> To: Vincy Pyne
> Cc: r-help at 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_pyne at 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]]
>>
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>
>        [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help at 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