>At 08:16 AM 12/14/2001, Ken Coar wrote: >>Here's a question that popped into my head a few days ago.. >> >>Are all quantities represented by base 10 integers irrational >>in base pi or base e?
At 11:12 AM 12/14/01, Richard S. Crawford wrote: >I'm not a mathematician by any stretch of the imagination, but I can only >ask how such numbers could not be irrational? Yes, it _seems_ reasonable, but _proving_ it can be a whole other kettle of fish. > Then, of course, there's my secondary question, which is how can you > have a counting system with an irrational number at the base in the first > place? <number> = d(n)*pi^n + d(n-1)*pi^(n-1) + . . . + d(2)*pi^2 + d(1)*pi + d(0) + d(-1)*pi^-1 + d(-2)* pi^(-2) + . . . where n is the larger of zero or the integer such that pi^n .le. <number> .lt. pi^(n-1), and the series formally does not terminate on the right, though it would be possible that all the d(i) = 0 after a certain point. The d(i) are what we call in base ten "digits," but since that term is sometimes considered only applicable in base ten, what shall we call them? "pigits", perhaps? (And similarly with e instead of pi.) >Then again, I'd probably better stop trying to figure this out before my >head melts. Oh, come on and join the fun! It's a lot easier after the meltdown. ;-) -- Ronn! :) ---------------------------------------------------------------------------- -- Ronn Blankenship Instructor of Astronomy/Planetary Science (and somewhere in there a masters degree in math, though I suppose my head melted long before I got that piece of paper) University of Montevallo Montevallo, AL, USA Standard Disclaimer (Does anyone ever read these things?): Unless specifically stated otherwise, any opinions stated herein are the personal opinions of the author and do not represent the official position of the University of Montevallo. -----------------------------------------------------------------------------
