2015/11/09 by László Németh · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Algebraic Geometry and Number Theory #Cube (algebra) #Generalization #Hyperbolic angle #Hyperbolic coordinates #Hyperbolic manifold #Hyperbolic tree #Hyperbolic triangle #Pascal (unit) #math.CO #math.MG #math.NT #msc:05B45 #msc:11B99 #msc:52C22
paper · pdf · doi:10.1007/s13366-016-0293-7
published as Beitr Algebra Geom 57 (2016) 913-927 · 14 pages, 10 figures
arxiv created 2015/11/09 · openalex publication_date 2016/05/05 · openalex created_date 2016/06/24 · arxiv updated 2017/03/17 · openalex updated_date 2026/08/05
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.