Re: Epistemology 201: The Science of Science
From: robert j. kolker (nowhere_at_nowhere.net)
Date: 03/04/05
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Date: Thu, 03 Mar 2005 19:05:55 -0500
Lester Zick wrote:
>
> And straight lines are still the shortest distance between points in
> Euclidean and non Euclidean geometries alike even if you can't
> traverse them.
A surface diffeomorphic to the surface of a sphere can be defined
without an embedding in E^3. That means just the surface exists without
the support of a large space. The shortest distances on this surface (or
manifold) is NOT euclidean distance.
Refer to any book in differential geometry for example -Lectures in
Classical Differential Geometry- by Dirk Struick.
Bob Kolker
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