Theos-Talk Archives (January 1997 Message tl00547)

> 
> Date: Fri Jan 17 01:32:49 1997
> From: John Straughn <JTarn@envirolink.org>
> To: theos-l@vnet.net
> Subject: Re: PI in the SKI digest 832
> Message-ID: <199701170632.BAA21942@envirolink.org>
> 
> Robert Word writes:
> >> From: John Straughn <JTarn@envirolink.org>
> >> Dr. A.M.Bain writes:
> >> >How about a mathematics in which we begin with "PI equals ONE."

Let C sub theta be the operation of rotating a planar object about the 
origin counterclockwise by theta radians.  Then (C sub PI) * (C sub PI) 
= 1.  Hence (C sub PI) is a root of unity, since rotating any object by 
2*pi radians will return the object.  Now (C sub theta) could be 
realized in n X n matrices, but if we suppose C sub theta is realized in 
real numbers, then we are forced to the conclusion

C sub pi = -1, since C sub pi is not the identity.

Now Dr. Bain, this is not the same as your equation

Pi = 1,

but at least its not far off.

However, your equation applies in the trivial universe.  By the trivial 
universe, I mean a number system in which every element is the identity 
element (i.e., there is only ONE THING).

With this hypothesis, we may quickly draw the conclusion

Pi = 1.

Now Dr. Bain, I have a little problem for you.  Let us go back to real 
numbers (and pi = 3.1415926...), and generalize the concept of "integer" 
to mean the class of numbers of the form

a + b*pi + c*(pi squared) + d*(pi cubed) + ... to a finite number of 
terms, where each of a,b,c... are rational numbers.

In this class of generalized integers, does the fundamental theorem of 
arithmetic hold true?  If not, can you find an exception to the 
fundamental theorem?  Please demonstrate by an example.



> >> >
> >> >Could be fun ...
> >> >
> >> >Burble burble burble ....
> >
> >I gather that you are not a mathematician.
>  I gather that you are not a pi-diatrician.

Yes, but I might be a kind of mathematician.

> >> You mean it doesn't?
> >>
> >> Blubber blubber blubber
> >
> >I gather that you are not a mathematician.

> ---
> The Triaist
>