Anyone remember Louisville numbers?
The simplest I recall is .110001000000000000000001000000... = sum of
0.1^(n!) for n=1,2,3,...
Many such numbers and constructions exist which share strange properties:
1) the digit patterns exist and are well-defined
2) the numbers, like pi, are transcendental [i.e., cannot be roots of any
polynomial in one variable with integer coefficients].
[Recall that the rational number p/q is a root of the "polynomial" qX - p
= 0.]
Showing pi transcendental takes a lot of effort. Showing the Louiville
numbers transcendental
takes a lot less effort (but maybe a lot more memory than I seem to have!).
Joth
----- Original Message -----
From: Philippe Trottier <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Wednesday, October 20, 1999 10:39 PM
Subject: Mersenne: RE: PI and other periods
> HI,
>
> Again if you look from a human eye, we can see (imagine) a nearly possible
> period in that number ..., again that's human brain doing overtime... But
> again MAYBE, there is a real period to that number... and this number also
> start to have a considerable amount of known digits (We would have to
share
> multiple generation just to say it)
>
> Philippe
>
> At 12:09 20.10.1999 +0100, you wrote:
> >Value of pi is the product of the infinite series ...
> >
> >pi = 4 (1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 -1/15 + 1/17.........)
> >
> >Hope this helps..
> >
> >Regards,
> >Ian McLoughlin, Chematek U.K.
> >
> >Tel/Fax : +44(0)1904 679906
> >Mobile : +44(0)7801 823421
> >Website: www.chematekuk.co.uk
>
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