User talk:Rmilson
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[edit]Hi Rmilson. Please don't have a go at me on AfD - assume good faith and all that. I'm just following procedure where speedy delete and PROD tags have been removed, which is to send the articles to AfD to allow the community to come to a consensus and the author of the articles to explain any reasoning for keeping them. It isn't a vote, it's a discussion, so assuming any motivation in me where there is none helps no-one. Thanks. ➨ ❝REDVERS❞ 10:44, 24 April 2006 (UTC)
No worries. I didn't mean for my comment to come across as overly adversarial, but I did want to contest your assertions. I will try for a different choice of wording. Rmilson 10:47, 24 April 2006 (UTC)
In mathematics, a manifold is an abstract multi-dimensional space where one cannot meaningfully make a choice of coordinate system. In contrast to Euclidean space , one cannot distinguish between a straight line and a curve, nor define the distance between two points. Another difference is that many manifolds possess a complicated spatial structure when viewed as a whole. There are finitary manifolds that are nonetheless unbounded ; other manifolds possess holes, regions where a circle cannot be continuously shrunk to a point.
The surface of Earth is an example of a manifold; locally it seems to be flat, but viewed as a whole it is round. However, since manifold geometry aims to be a minimalist theory, the surface of a sphere and the surface of an ellipsoid cannot be distinguished as manifolds. A manifold can be constructed by "gluing" separate Euclidean spaces together; for example, a world map can be made by gluing many maps of local regions together, and accounting for the resulting distortions. Alternatively, a manifold can be defined by a system of equations. However, as a geometric entity in and of itself, a manifold exists independently of any ambient space.