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Question by  kat43netzerocom (52)

# What are the differences in euclidean versus non-euclidean geometry?

 +1 vote! +4 you voted Answer by  pdg (19) Euclidean geometry assumes that shapes exist on flat planes. The angles in a triangle in euclidean geometry sum up to 180 degrees. Non-euclidean geometry deals with shapes that exist in curved space, such as on the surface of a sphere. In this kind of space, a triangle's angles can add up to more than 180 degrees.

 +1 vote! +3 you voted Answer by  Robert20 (51) Euclidian geometry refers to geometry dealing with lines and segment of lines. Non-euclidian geometry refers to geometries that does not satisfy the parallel postulate, e. g. hyperbolic or elliptic.

 +1 vote! +3 you voted Answer by  BrianSJ (524) The most important difference is that Euclidean geometry occurs on an endless plane, without curvature. The different Non-Euclidean geometries are also intended to cover geometry for curved planes and spaces as well as non-curved spaces.

 +1 vote! +3 you voted Answer by  ricky (25) Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria. A non-Euclidean geometry is characterized by a non-vanishing Riemann curvature tensor.