Pascal pyramid in the space H2×R

László Németh

Vol. 22 No. 2 (2017)

Regular Articles

Pascal pyramid in the space H2×R

Published 2017-02-17

László Németh

László Németh
University of Sopron

Submission of an original manuscript to the Mathematical Communications will be taken to mean that it represents original work not previously published, that it is not being considered elsewhere for publication; and, if accepted for publication, it will be published in print and online form and it will not be published elsewhere in the same form, for commercial purposes, in any language, without the consent of the publisher. The journal takes the stance that the publication of scholarly research is meant to disseminate knowledge and, in a not-for-profit regime, benefits neither publisher nor author financially. It sees itself as having an obligation to its authors and to society to make content available online now that the technology allows for such a possibility.

Abstract

In this article we introduce a new type of Pascal pyramids. A regular squared mosaic in the hyperbolic plane yields an (h2r)-cube mosaic in space H2R 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

PDF

Supplementary File(s)

LaTeX file Fig_BW