Euclidean and Non Euclidean Space?

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Euclidean space adheres to Euclid's axioms, characterized by flat geometry where parallel lines never intersect. Non-Euclidean space arises when one or more of these axioms are violated, leading to curved geometries, such as spherical or hyperbolic spaces. The term 'flat' refers to the absence of curvature, indicating that the geometry behaves according to Euclidean principles. Gauss's work in surveying highlighted the practical implications of these concepts in real-world applications. Understanding these distinctions is crucial for grasping advanced mathematical and physical theories.
sepulshan
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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
 
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You know Euclids axioms for geometry, right? Well, a space is Euclidean if and only if all of them hold. :-p

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

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