[longshadow]

So a manifold is a Euclidean description of a non-Euclidean space?

I'm not clear on what you mean by "Euclidean description"....

The simplest way I can think to say it is a manifold is a topological space which locally Euclidean. That is to say the space appears to be Euclidean if you don't stray too "far" away from the point you are examining.

I put "far" in parens because not all topological spaces have a notion of "distance" (as best I recall)....

[PatrickHenry]

... not all topological spaces have a notion of "distance" (as best I recall)....

I try to stay away from such places.

[tcuoohjohn]

I mean "is a manifold a Euclidean ( Planar) description of a Non-Euclidean ( curvilinear) space or form."?

Eg. Does Topology describe in a Euclidean way, by use of discreet cumulative adjacent planes a non-euclidean form?

Hope I'm making some sense here..as you can tell I am no mathematician so I have to use imprecise words and phrases to describe what I mean.