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
You're welcome to join The Smarandache
Geometries group.
Smarandache Geometries (1, 2, 3, 4)
Books:
|
|
Smarandache Geometries & Map Theories with Applications (I), by. L. Mao new |
|
|
|
|
|
|
|
|
Articles:
