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

From: J.Barsuhn (jw.barsuhn_at_t-online.de)
Date: 09/21/04 

Date: Tue, 21 Sep 2004 03:55:35 +0200

Dear Tim,

thank you for your answer.
What I would be interested especially is whether some of the irrational
numbers a beginning student would hit have this property (of containing
any previously defined sequence of digits somewhere in its decimal
representation): Numbers like sqrt(2) or the Euler e. If I interpret
Carlīs (Devore) posting correctly, he says yes.

Tim Brauch schrieb:
> "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...
>
...indeed this number has been discussed in this newsgroup under the
name "iota". With respect to my question it is a "counter-example" in
the sense that even "most" strings consisting of 1 and 0 do not occur in
iota.

> 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

All the best Jurgen

>

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