It is the same thing (simply multiply the polynomial by the LCM and you have a polynomial with integer coefficients).
------------------------------------------------------- Ravi Varadhan, Ph.D. Assistant Professor, Division of Geriatric Medicine and Gerontology School of Medicine Johns Hopkins University Ph. (410) 502-2619 email: [email protected]<mailto:[email protected]> From: [email protected] [mailto:[email protected]] Sent: Tuesday, May 31, 2011 11:06 AM To: Ravi Varadhan Cc: 'Bentley Coffey'; [email protected]; [email protected]; Vincy Pyne Subject: Re: [R] Value of 'pi' A transcendental number is not the zero of any polynomial with <rational>, not just integer, coefficients . Ravi Varadhan <[email protected]> Sent by: [email protected] 05/31/2011 10:12 AM To "'Bentley Coffey'" <[email protected]>, Vincy Pyne <[email protected]> cc "[email protected]" <[email protected]> Subject Re: [R] Value of 'pi' `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: [email protected] -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Bentley Coffey Sent: Monday, May 30, 2011 9:01 PM To: Vincy Pyne Cc: [email protected] 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" <[email protected]> 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]] > > ______________________________________________ > [email protected] 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]] ______________________________________________ [email protected] 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. ______________________________________________ [email protected] 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]] ______________________________________________ [email protected] 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.
