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Pascal pyramid in the space \( H^{2}\) xR

László Németh orcid.org/0000-0001-9062-9280 ; University of Sopron, Institute of Mathematics, Sopron, Hungary

Sažetak

In this article we introduce a new type of Pascal pyramids. A regular squared mosaic in the hyperbolic plane yields an \( h^{2}r\)-cube mosaic in space \( H^{2}\) xR and the definition of the pyramid is based on this regular mosaic. The levels of the pyramid inherit some properties from the Euclidean and hyperbolic Pascal triangles. We give the growing method from level to level and show some illustrating figures.

Ključne riječi

Pascal's triangle; hyperbolic Pascal triangle; Pascal pyramid; regular mosaics; cubic honeycomb; Thurston geometries; prism tiling in space H2R; recurrence sequences

Hrčak ID:

185975

URI

https://hrcak.srce.hr/185975

Datum izdavanja:

4.12.2017.

Posjeta: 1.407 *