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

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.

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.

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.

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.