creepy numbers

Can Gene or anyone shed light on this phenomenon:

(999999/127000)^2 = 62.00000000006200 . . .

?

--- In metatuning@yahoogroups.com, "Paul Erlich" <PERLICH@A...> wrote:
> Can Gene or anyone shed light on this phenomenon:
>
> (999999/127000)^2 = 62.00000000006200 . . .

1000/127 is a convergent for sqrt(62), and (1000/127)^2 = 1000000/16129
= 62000000/999998 = 62000000/(1000000-2) = 62(1/(1-2/1000000)) =
62(1 + 2*10^(-6) + 4*10^(-12) + ...)

We can now correct 1000/127 to get a more accurate square root; since
(1000/127) ~ 62(1+2*10^(-6)), if we take (1-10^(-6))(1000/127) for the
square root, which is 999999/127000, we get rid of the first-order
error. The series expansion now becomes

62(1-10^(-6))^2(1+2*10^(-6)+4*10^(-12) + ...) =
62(1+*10^(-12)+2*10^(-18)+....)

where the series terms are what you get by substituting x=10^(-6) in
the power series expansion of (1-x)^2/(1-2*x) = 1+x^2+2*x^3+4*x^4+...

Now that I've worked all that out, I'm wondering what good it all is.

If you want something creepy to contemplate, you might try to evaluate

exp((pi/3)*sqrt(163)) ~ 640320

The reasons this is approximately an integer lie much deeper than the
creepy stuff above.

--- In metatuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> If you want something creepy to contemplate, you might try to
evaluate
>
> exp((pi/3)*sqrt(163)) ~ 640320
>
> The reasons this is approximately an integer lie much deeper than
the
> creepy stuff above.

Yeah, I remember trying to follow threads on the above on the
internet on a number of occasions.

--- In metatuning@yahoogroups.com, "Paul Erlich" <PERLICH@A...> wrote:
> --- In metatuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> > If you want something creepy to contemplate, you might try to
> evaluate
> >
> > exp((pi/3)*sqrt(163)) ~ 640320
> >
> > The reasons this is approximately an integer lie much deeper than
> the
> > creepy stuff above.
>
> Yeah, I remember trying to follow threads on the above on the
> internet on a number of occasions.

You've got to read my Wikipedia artile "j invariant" first. :)

--- In metatuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In metatuning@yahoogroups.com, "Paul Erlich" <PERLICH@A...>
wrote:
> > --- In metatuning@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...>
> > wrote:
> >
> > > If you want something creepy to contemplate, you might try to
> > evaluate
> > >
> > > exp((pi/3)*sqrt(163)) ~ 640320
> > >
> > > The reasons this is approximately an integer lie much deeper
than
> > the
> > > creepy stuff above.
> >
> > Yeah, I remember trying to follow threads on the above on the
> > internet on a number of occasions.
>
> You've got to read my Wikipedia artile "j invariant" first. :)

Can't find it. URL?

--- In metatuning@yahoogroups.com, "Paul Erlich" <PERLICH@A...> wrote:
> --- In metatuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > --- In metatuning@yahoogroups.com, "Paul Erlich" <PERLICH@A...>
> wrote:
> > > --- In metatuning@yahoogroups.com, "Gene Ward Smith"
> <gwsmith@s...>
> > > wrote:
> > >
> > > > If you want something creepy to contemplate, you might try to
> > > evaluate
> > > >
> > > > exp((pi/3)*sqrt(163)) ~ 640320
> > > >
> > > > The reasons this is approximately an integer lie much deeper
> than
> > > the
> > > > creepy stuff above.
> > >
> > > Yeah, I remember trying to follow threads on the above on the
> > > internet on a number of occasions.
> >
> > You've got to read my Wikipedia artile "j invariant" first. :)
>
> Can't find it. URL?

Found it -- http://en.wikipedia.org/wiki/J-invariant . . . seems you
have an "of" missing in ". . . are the dimensions of the grade n part
an infinite dimensional graded algebra representation of . . ." . . .

--- In metatuning@yahoogroups.com, "Paul Erlich" <PERLICH@A...> wrote:

> Found it -- http://en.wikipedia.org/wiki/J-invariant . . . seems
you
> have an "of" missing in ". . . are the dimensions of the grade n
part
> an infinite dimensional graded algebra representation
of . . ." . . .

Thanks! A special bonus goes to anyone who can relate Moonshine
Theory to music somehow. Ogg's original prize was a fifth of Jack
Daniels; I'll have to think of what would be appropriate.

--- In metatuning@yahoogroups.com, "Paul Erlich" <PERLICH@A...> wrote:
> --- In metatuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
>
> > If you want something creepy to contemplate, you might try to
> evaluate
> >
> > exp((pi/3)*sqrt(163)) ~ 640320
> >
> > The reasons this is approximately an integer lie much deeper than
> the
> > creepy stuff above.
>
> Yeah, I remember trying to follow threads on the above on the
> internet on a number of occasions.

Check this out:

http://mathworld.wolfram.com/AlmostInteger.html

on 2/27/04 7:55 PM, Gene Ward Smith <gwsmith@...> wrote:

> --- In metatuning@yahoogroups.com, "Paul Erlich" <PERLICH@A...> wrote:
>
>> Found it -- http://en.wikipedia.org/wiki/J-invariant . . . seems
> you
>> have an "of" missing in ". . . are the dimensions of the grade n
> part
>> an infinite dimensional graded algebra representation
> of . . ." . . .
>
> Thanks! A special bonus goes to anyone who can relate Moonshine
> Theory to music somehow. Ogg's original prize was a fifth of Jack
> Daniels; I'll have to think of what would be appropriate.

The "moonshine theory" link on this page:

http://en.wikipedia.org/wiki/J-invariant

somehow appears to point to:

http://en.wikipedia.org/w/wiki.phtml?title=Moonshine_theory&action=edit

which indicates that the page does not exist.

-Kurt

--- In metatuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 2/27/04 7:55 PM, Gene Ward Smith <gwsmith@s...> wrote:

> The "moonshine theory" link on this page:
>
> http://en.wikipedia.org/wiki/J-invariant
>
> somehow appears to point to:
>
> http://en.wikipedia.org/w/wiki.phtml?
title=Moonshine_theory&action=edit
>
> which indicates that the page does not exist.

I know. I was going to try to write a page, but moonshine theory is
hard to explain if you really intend to give the relevant details.