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On the hyperbolic Pascal pyramid

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Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry Aims and scope Submit manuscript

Abstract

In this paper we introduce a new geometric object called hyperbolic Pascal pyramid. This new object is presented by the regular cube mosaic (cubic honeycomb) in the hyperbolic space. The definition of the hyperbolic Pascal pyramid, whose faces are hyperbolic Pascals triangles, is a natural generalization of the definition of the hyperbolic Pascal triangle (Belbachir et al. in Appl Math Comput 273:453–464, 2016) and Pascal’s arithmetic pyramid. We describe the growing of the hyperbolic Pascal pyramid considering the numbers and the values of the elements. Further figures illustrate the stepping from a level to the next one.

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References

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Authors and Affiliations

  1. Institute of Mathematics, University of West Hungary, Sopron, Hungary

    László Németh

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  1. László Németh
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Németh, L. On the hyperbolic Pascal pyramid. Beitr Algebra Geom 57, 913–927 (2016). https://doi.org/10.1007/s13366-016-0293-7

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  • DOI: https://doi.org/10.1007/s13366-016-0293-7

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