Splitting of 3d quaternion dimensions into 2d-sells and a "world screen technology"

Details Splitting of 3d quaternion dimensions into 2d-sells and a "world screen technology" Splitting of 3d quaternion dimensions into 2d-sells and a "world screen technology"

2012-02-14

arxiv.org/abs/1202.2995v1

Advanced Science Letters, 2012, Volume 5, 288-293

Physics

General Physics

12 pages

Scientific paper

A set of basic vectors locally describing metric properties of an arbitrary 2-dimensional (2D) surface is used for construction of fundamental algebraic objects having nilpotent and idempotent properties. It is shown that all possible linear combinations of the objects when multiplied behave as a set of hypercomples (in particular, quaternion) units; thus interior structure of the 3D space dimensions pointed by the vector units is exposed. Geometric representations of elementary surfaces (2D-sells) structuring the dimensions are studied in detail. Established mathematical link between a vector quaternion triad treated as a frame in 3D space and elementary 2D-sells prompts to raise an idea of "world screen" having 1/2 of a space dimension but adequately reflecting kinematical properties of an ensemble of 3D frames.

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