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One main characteristic of non-Euclidean geometry is hyperbolic geometry. The other is elliptic geometry. Non-Euclidean geometry is still closely related to Euclidean geometry.
The geometry of similarity in the Euclidean plane or Euclidean space.
true
There are two non-Euclidean geometries: hyperbolic geometry and ellptic geometry.
Euclid developed Euclidean geometry around 300 BC. I cannot get much briefer than that.