From: Marko Vojinovic <vvmarko(a)gmail.com>
Subject: Re: how to generate pi in c
To: "Community support for Fedora users" <users(a)lists.fedoraproject.org>
Date: Monday, November 8, 2010, 3:27 PM
On Monday, November 08, 2010 18:00:55
Bruno Wolff III wrote:
> > On Monday, November 08, 2010 04:49:33 Tim wrote:
> > > On Sat, 2010-11-06 at 17:13 +0100,
Klaus-Peter Schrage wrote:
> > > > You are probably alle wrong - pi equals
3.125, see:
> > > >
http://www.correctpi.com/
> > >
> > > I was always under the impression that pi
was merely the ratio of the
> > > circumference to the diameter, something
that's easy enough to prove
> > > empirically (measure the two, and do the
maths).
>
> Just remember that depends on Euclidean Geometry. In
other geometries (say
> very large circles on the surface of the earth) the
ratio is different.
Ok, well, since this thread is already so far off-topic for
a Fedora list, it
won't hurt much to add a few more lines... :-)
The pi can actually be defined as a period of the
exponential function, exp(z),
in the imaginary direction. This is quite fundamental, and
doesn't depend on
any geometry definition whatsoever. Everything else can be
considered a
consequence, if you set up your axioms in a convenient
way... ;-)
e^{i\pi} + 1 = 0
\pi = (\ln(-1)/i), but \ln(-1) does not exist? in the Real Numbers, and i = \sqrt(-1).
Interesting, indeed :)