English

Hyperbolic Pascal pyramid

Combinatorics 2017-03-17 v2 Metric Geometry Number Theory

Abstract

In this paper we introduce a new type of Pascal's pyramids. The new object is called hyperbolic Pascal pyramid since the mathematical background goes back to the regular cube mosaic (cubic honeycomb) in the hyperbolic space. The definition of the hyperbolic Pascal pyramid is a natural generalization of the definition of hyperbolic Pascal triangle and Pascal's arithmetic pyramid. We describe the growing of hyperbolic Pascal pyramid considering the numbers and the values of the elements. Further figures illustrate the stepping from a level to the next one.

Keywords

Cite

@article{arxiv.1511.02067,
  title  = {Hyperbolic Pascal pyramid},
  author = {László Németh},
  journal= {arXiv preprint arXiv:1511.02067},
  year   = {2017}
}

Comments

14 pages, 10 figures

R2 v1 2026-06-22T11:38:58.786Z