Original scientific paper
Pascal pyramid in the space \( H^{2}\) xR
László Németh
orcid.org/0000-0001-9062-9280
; University of Sopron, Institute of Mathematics, Sopron, Hungary
Abstract
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.
Keywords
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
Publication date:
4.12.2017.
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