Re: "Almost" an Integer - e^?

Jyrki Lahtonen <[EMAIL PROTECTED]> wrote in message news:<[EMAIL PROTECTED]>...
> TCL wrote:
> > 
> > I remember there is an explanation for these numbers.
> > Anyone knows where to find the reference (books better)?
> > 
> E.g. J.Silverman, "Advanced Topics in the Arithmetic of Elliptic 
> Curves" or something like that (Springer GTM series) has the
> explanation involving class fields and their relations to the
> j-invariant. There may be other explanations.
> 
> Cheers,
> 
> Jyrki Lahtonen

On the much lighter side ---
Another interesting fact about e^(pi * sqrt(163)) is ---

If you add this large composite reciprocal to 163 which is a (29)
digit long integer ---

e^(pi * sqrt(163 + (1/43072298941682041177938098750)))  =
262537412648768743.999999999999999999999999999999999999999998219574092..

Gives (41) 9's in its decimal expansion. 

More interesting is --

e^(1/43072298941682041177938098750) =

1.000000000000000000000000000023216777942...

Where if you -1 from the above ---  =

1/43072298941682041177938098750  ;-)  

Probably the largest integer reciprocal that could be added to 163
giving the same floor (value) of the original (e^(pi * sqrt(163))) and
producing a limit of (41) 9‘s in the decimal expansion compared to
(12) 9's in the original.


Dan