An Introduction to the Smarandache Geometries
by
Mike Antholy
University of Toronto

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). 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. See a club about these geometries at http://clubs.yahoo.com/clubs/smarandachegeometries .

http://clubs.yahoo.com/clubs/smarandachegeometries

Date received: September 14, 2001