Dr. Dobb's Python-URL! - weekly Python news and links (Mar 17)

Tim Peters tim.one at comcast.net
Wed Mar 19 02:05:01 CET 2003


[Greg Ewing]
> Just out of curiosity, has any other irrational
> number (other than ones specially constructed to
> be so) been proved normal?

Last I heard (a few years ago), no.  Note two meanings for "normal":  the
original definition required normality in all bases simultaneously, and
that's usually called "absolutely normal" now.  Also, AFAIK, no absolutely
normal number is known (constructed or not).  This is curious because the
set of non-normal reals has measure 0 ("almost all" reals are absolutely
normal).

> And what are the grounds for suspecting pi to
> be normal? Is it just "we don't have any particular
> reason to think it isn't", or is there more to
> it?

Billions of digits of pi have been computed, and this tiny string of digits
has passed extensive statistical tests for equidistribution (of single
digits, pairs, triples, ..., up to something like 16-tuples).  By induction,
it must be normal <wink>.






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