Euclidean and Non Euclidean Space?

[sepulshan]

Hi

Can someone explain the difference between Euclidean and Non Euclidean Space and how does one classify a space as Euclidean or Non Euclidean?? I heard about Gauss coming up with Non Euclidean Spaces when he was doing surveying of a piece of land. I am wondering what the word 'FLAT' really means??Any examples or references would be appreciated..

Regards
Shankar

 

[Hurkyl]

You know Euclids axioms for geometry, right? Well, a space is Euclidean if and only if all of them hold.

(well, Euclid missed a couple axioms, but you get the point)