Smarandache Geometries & Map Theory with Applications (I)


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This page provides a list of all articles available at PlanetMath in the following topic: XX Differential geometry. This list will be periodically updated.

Florentin Smarandache | DeepAI

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Views Read Edit View history. A Smarandache Geometry is a geometry which has at least one smarandachely denied axiom 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. These geometries connect many geometrical spaces with different structures into a heterogeneous multispace with multistructure.

In particular, a Smarandache geometry is such a geometry in which there is at least one Smarandachely denied rule, and a Smarandache manifold M;A is an n-dimensional manifold M that supports a Smarandache geometry.


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In a Smarandache geometry, the points, lines, planes, spaces, triangles, Howard Iseri constructed the Smarandache 2-manifolds by using equilateral triangular disks on Euclidean plane R 2. Such manifold came true by paper models in R 3 for elliptic, Euclidean and hyperbolic cases. It should be noted that a more general Smarandache n -manifold, i.


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  5. A curve in a Smarandache Geometry is called Smarandache Curve. China, ]. Smarandache Geometries paradoxist , non-geometry , counter-projective , anti-geometry.

    A new view of combinatorial maps by Smarandache's notion, by L. Neutrosophic Environment.


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