Geometries
An axiom is said smarandachely denied if in the same space the axiom behaves
differently (i.e., validated and invalided; or only invalidated but in at least
two distinct ways).
Therefore, we say that
an axiom is partially negated, or there is a degree of negation of an axiom.
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 geometry in a subspace) and with the Parallel
Universes.
Paper abstracts
were submitted online to the First
International Conference on Smarandache Geometries, that was held between
3-5 May, 2003, at the
An Introduction to the Smarandache Geometries, paper
by M. Antholy, was presented to the
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Smarandache Geometries (1, 2, 3, 4)
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