Re: OT: White Goddess

On Wed, 11 Apr 2001, Andreas Johansson wrote:

> > >    Think of truth and fact like circles and squares -
> > > a square is a circle, with sufficient numbers of sides
> > > (or however that saying goes - I know I got it wrong).
> >
> >Wrong.  A square is a polygon.  A circle is beyond a polygon.  It has
> >transcended infinity.  You cannot give a polygon enough sides to *be* a
> >circle, it can only *approach* a circle.  The difference is not merely a
> >matter of degree.
>
> Eh, seeing that I supposed to be good at math, I should probably know this
> myself, but what's the difference between a circle and a regular polygon
> with an infinite number of sides? I definitely recall being told by my math
> teacher tellin' me they're the same ...
Suppose you have a regular polygon with n sides.  (I think you could get
by with a weaker condition but this will suffice.)  The "limit" of the
polygon as n goes to infinity is a circle.

I am not certain what mathematical meaning, if any, "transcended
infinity" has, though.

In a sense, I suppose you're both right.  If you just sit there adding
sides to a polygon you'll sit there forever.  ^_^  Also, it depends on
whether you're talking geometry and ideal shapes (in which case you could
hit the circle) or the "real world" where eventually Planck length and
practicality would kick in.  Even our best circles are approximations if
you magnify them large enough...but for most practical purposes, I
suspect "a polygon with 100 million sides" would be a quite adequate
"circle."

YHL, remembering geometry

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