Re: Arbitrary strings of digits in the decimal display of Pi

From: Tim Brauch (RnEeMwOs.pVoEst_at_tbrauch.cNOoSPAMm)
Date: 09/20/04 

Date: Mon, 20 Sep 2004 05:08:02 GMT

"J.Barsuhn" <jw.barsuhn@t-online.de> wrote in
news:414E1ECA.3060300@t-online.de:

 
> Are there other irrational numbers that are expected to exhibit this
> same property? Of course, this cannot be a general property of
> irrational numbers.

You can always create irrational numbers to satisfy certain properties that
you want. A somewhat classic example (at least I've come across it enough
in texts):

1.101001000100001000001...

It is irrational yet very easy to understand, first there is no zeroes
between the ones, then one zero, then two, then three, and so on. No
matter how hard you look, this number will never contain the digit "2."
You can create an infinite (uncountable?) set of examples playing with this
idea to have (almost) any properties. Try this one...

3.31 314 3141 31415 314159 3141592 314145926...

Interestingly, you can find every single digit of pi in this number. And,
any sequence of digits you can find in pi, you can find infinitely many
times in this number.

 - Tim 

-- 
Timothy M. Brauch
NSF Fellow
Department of Mathematics
University of Louisville
email is:
news (dot) post (at) tbrauch (dot) com

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