🚀 go-pugleaf

Martin Ward wrote:
> 
> In article <5hhge0$48q@raven.cc.ukans.edu>, Greffindel
> <ipsifend@eagle.cc.ukans.edu> writes
> >Jonathan Cunningham (jlc@sofluc.demon.co.uk) wrote:
> -- snip --
> >: Be careful if you are determining pi by measuring the ratio of the
> >: circumference of a circle to its diameter: a one tonne weight in a 10 metre
> >: diameter circle will affect the value of pi in about the 24th or 25th
> >: decimal place (general relativity and curvature of space-time etc.). If
> >: you wish to try this, it's worth knowing that the correct value of
> >: pi should be around 3.14159265358979323846264338 in flat space, although
> >: the last two or three digits will be different with the one tonne weight
> >: in place. :-).
> >
> >: Jonathan
> >
> >(thinks) (thinks) (thinks)  You know, that makes sense.  What could
> >you say about the set of weights such that under their influence, the
> >"effective pi" would become rational?  Algebraic? How big a weight
> >would you need to get a "pi" of 4?
> >
> >--
> >--Greffindel the Plaid
> 
> Jonathan obviously understands the physics of this better than I do, but
> putting in a weight must *reduce* the local "pi", surely?
> 
> Since there are algebraic and rational numbers arbitrarily close to any
> transcendental number like pi the same would be true of the set of
> values of our central mass.  If we can assign it a random real value
> then most such would leave "pi" transcendental, but we could find
> infinitely many values within any range >0 which make "pi" rational.
> 
> Of course quantum mechanics says, does it not, that masses cannot be
> given an arbitrary real value but only one chosen from a set of discrete
> values....
> --
> 
> Martin Ward
> 
> 

Hmmmm, hadn't thought of Pi as dependent on local conditions, but of
course it's true.

Suppose the one ton weight was a singularity with an mass x and an
effective diameter of 1 millimetre. This could be easily drawn and
visualised but how would you work out the radius/circumfrence.

Also, if my memory serves, object travelling at very near "c" will be
"stretched" along the axis of travel, so the orientation of a circle to
said axis would presumably affect pi, or maybe not as it would no longer
be a circle.

OK, my head hurts.

JB