An axiom is said Smarandachely denied if the axiom behaves in at least two different ways within the same space (i.e., validated and invalided, or only invalidated but in multiple ways).
A SMARANDACHE GEOMETRY is a geometry which has at least one Smarandachely denied axiom (1969).
Thus, as a particular case, Euclidean, Lobachevsky-Bolyai-Gauss, and
Riemannian geometries may be united altogether, in the same
space, by some Smarandache geometries.
These last geometries can be partially Euclidean and partially
Non-Euclidean.
It seems that Smarandache Geometries are connected with the
Theory of Relativity (because they include the Riemannian
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