The fulfilled Euclidean plane.(Report)

From: Smarandache Notions Journal | Date: January 1, 2004| Author: | Copyright information

ABSTRACT. The fulfilled euclidean plane is the real projective plane [bar.[PI]] completed with the infinite point of its infinite line denoted [[bar.[PI]].sup.c]. This new incidence structure is a structure with neighbouring elements, in which the unicity of the line through two distinct points is not assured. This new Geometry is a Smarandacheian structure introduced in (10) and [11], which generalizes and unites in the same time: Euclid, Bolyai Lobacewski Gauss and Riemann Geometries.

Key words: Non-euclidean Geometries, Hjelmslev-Barbilian Geometry, Smarandache Geometries, ...

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