Hyperbolic Pascal simplex
نویسندگان
چکیده
In this article we introduce a new geometric object called hyperbolic Pascal simplex. This new object is presented by the regular hypercube mosaic in the 4-dimensional hyperbolic space. The definition of the hyperbolic Pascal simplex, whose hyperfaces are hyperbolic Pascal pyramids and faces are hyperbolic Pascals triangles, is a natural generalization of the definition of the hyperbolic Pascal triangle and pyramid. We describe the growing of the hyperbolic Pascal simplex considering the numbers and the values of the elements. Further figures illustrate the stepping from a level to the next one.
منابع مشابه
Hyperbolic Pascal pyramid
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 ([2]) and Pascal’s arithmetic pyramid. We descri...
متن کاملFibonacci words in hyperbolic Pascal triangles
The hyperbolic Pascal triangle HPT 4,q (q ≥ 5) is a new mathematical construction, which is a geometrical generalization of Pascal’s arithmetical triangle. In the present study we show that a natural pattern of rows of HPT 4,5 is almost the same as the sequence consisting of every second term of the well-known Fibonacci words. Further, we give a generalization of the Fibonacci words using the h...
متن کاملar X iv : m at h / 03 01 08 6 v 1 [ m at h . A G ] 9 J an 2 00 3 Maximal rank root subsystems of hyperbolic root systems
A Kac-Moody algebra is called hyperbolic if it corresponds to a generalized Cartan matrix of hyperbolic type. We study root subsystems of root systems of hyperbolic algebras. In this paper, we classify maximal rank regular hyperbolic subalgebras of hyperbolic Kac-Moody algebras. Introduction A generalized Cartan matrix A is called a matrix of hyperbolic type if it is indecomposable symmetrizabl...
متن کاملOn Subgroup Separability in Hyperbolic Coxeter Groups
We prove that certain hyperbolic Coxeter groups are separable on their geometrically ¢nite subgroups. Mathematics Subject Classi¢cation (2000). 20H10. Key words. hyperbolic Coxeter group, subgroup separability. 1. Introduction Recall that a subgroupH of a group G is separable in G if, given any g 2 G nH, there exists a subgroup K < G of ¢nite index with H < K and g = 2K . G is called subgroup s...
متن کاملar X iv : m at h / 99 07 13 9 v 1 [ m at h . G T ] 2 2 Ju l 1 99 9 CONSTRUCTING HYPERBOLIC MANIFOLDS
The Coxeter simplex with symbol is a compact hyperbolic 4-simplex and the related Coxeter group Γ is a discrete subgroup of Isom(H 4). The Coxeter simplex with symbol is a spherical 3-simplex, and the related Coxeter group G is the group of symmetries of the regular 120-cell. Using the geometry of the regular 120-cell, Davis [3] constructed an epimorphism Γ → G whose kernel K was torsion-free, ...
متن کامل