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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


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


Papers, notes, comments are welcome and

will be published in a collection book.

See: http://www.gallup.unm.edu/~smarandache/geometries.htm

Group Information

  • 168
  • Geometry
  • Jul 26, 2001
  • English

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