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Polyangles and their symmetries in H3
2009jaw | D.G. Pavlov, S.S. Kokarev  // Research Institute of Hypercomplex Numbers in Geometry and Physics, Friazino, Russia, RSEC "Logos", Yaroslavl, logos-center@mail.ru

We construct bingles and tringles in 3D Berwald-Moor space as additive characteristics of pairs and triples of unit vectors -- lengths and squares on unit sphere (indicatrix). Two kind of bingles (mutual and relative) can be determined analogously to spherical angles $\theta$ and $\varphi$ respectively. We show that mutual bingle is, in fact, norm in space of exponential bingles (bi-space $H_3^{\flat}$), which define exponential representation of polynumbers. It is turned out, that metric of bi-space is the same Berwald-Moor ones. Relative angles are connected with elements of second bi-space $(H_3^{\flat})^{\flat}$ and give possibility for two-fold exponential representation of polynumbers. Apparent formulae for relative bingles and tringles contain non-elementary integrals.


English: Russian:
11-04.pdf, 1291,72 Kb, PDF
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