The question refers to the "following". In such circumstances would it be too much to expect that you make sure that there is something that is following?
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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.
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Euclidean geometry, non euclidean geometry. Plane geometry. Three dimensional geometry to name but a few