From: Damien Broderick (d.broderick@english.unimelb.edu.au)
Date: Sat Mar 09 2002 - 17:43:25 MST
At 09:31 AM 3/9/02 -0800, Spike wrote:
> In any universe with any curvature, a circle would still
> have 360 degrees, for the circle defines the degree, as well as the radian.
> The expansion given would work even in a different space curvature,
Yet it is a commonplace that in Bolyai and Lobachevski spaces, the internal
angles of triangles sum to less than 180 degrees, and in Riemann space they
sum to more than 180. Euclid would have insisted that the *definition* of
`triangle' included the 180-degree sum. Sure you're not doing that with
circles? (I mean, sure, if we agree that circles by definition contain just
360 degrees, that must always be true, as long as we can then say that the
size of a degree changes according to the space it's measured in--which
seems a rather perverse metric. We could squeeze the Celsius range
freezing-to-boiling at the top of a mountain, so that you could happily put
your hand into 100 degree water, but that's too relativist for my tastes.)
Damien Broderick
[kind of physicist either]
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