From: Andrew Clough (aclough@mit.edu)
Date: Tue Mar 12 2002 - 10:14:08 MST
At 11:04 AM 3/12/2002 -0500, you wrote:
>Ken Clements wrote:
>
> > I covered the spherical case in my post. Yes, the ratio changes with
> curvature, but pi does not change. Again, the ratio is simply no longer
> equal to pi.
>
>When pi is no longer equal to that ratio, how does pi deserve to be
>called pi? Pi is defined as that ratio, ergo its value is relative to
>the local time space curvature.
I believe somebody already mentioned on this topic that pi is generally
defined as the ratio of a circle's circumference to its diameter in
Euclidean geometry. Because of Euclid's fifth postulate (1) space is never
curved in Euclidean geometry, though, so though pi is defined by the ratio,
that doesn't really matter here.
1: If two lines are drawn which intersect a third in such a way that the
sum of the inner angles on one side is less than two right angles, then the
two lines inevitably must intersect each other on that side if extended far
enough.
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